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The Extension of Analytic Hypersonic Force

Coefficients for Conceptual Design Using the

Divergence Theorem

Michael J. Grant and Robert D. Braun

Georgia Institute of Technology, Atlanta, GA, 30332

This study investigates the type and performance of analytic Newtonian aerodynamicsolutions made possible using the Divergence Theorem. A reformulation of the Newtoniansurface pressure calculation enables a mathematically equivalent divergence calculation tobe performed as a substitute. This manipulation enables analytic force coefficients to bederived for shapes of increasing complexity while also reducing computational cost whencompared to existing analytic solutions. The divergence solutions are obtained by con-verting the physical flow field into a mathematical flow field that is constant in directionbut with magnitude that is equivalent to the Newtonian pressure coefficient. This uniqueproperty allows various mathematical techniques that are not available with the traditionalNewtonian calculation to be performed that further reduce computational cost. The resultsof this investigation enable the construction of analytic relations for new hypersonic config-urations of interest, and this approach serves as the foundation to construct efficient hybridexact-approximate solutions for more complex configurations. Comparisons of the currentanalytic database to a state-of-the-art hypersonic design tool illustrate the computationaladvantages of the analytic relations to support hypersonic conceptual design.

Nomenclature

APAS Aerodynamic Preliminary Analysis SystemCBAERO Configuration Based AerodynamicsCFD Computational Fluid DynamicsHABP Hypersonic Arbitrary Body Program

A panel area, m2

Aref reference area, m2

CA axial force coefficientCN normal force coefficientCS side force coefficientCp pressure coefficientD volume domainp pressure on surface of body, Pap freestream pressure, Parn nose radius, mS surface domainV freestream velocity, m/s

df differential force, NF vector fieldn unit normal, mr surface position vector, m

angle of attack, radc cone angle, rad relative angle between body and flow, rad potential radius, m freestream density, kg/m

3

potential function revolution angle, rad

Graduate Research Assistant, Guggenheim School of Aerospace Engineering, AIAA Student Member.David and Andrew Lewis Associate Professor of Space Technology, Guggenheim School of Aerospace Engineering, AIAA

Fellow.

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American Institute of Aeronautics and Astronautics

I. Introduction

Traditionally, the hypersonic aerodynamics of vehicles are modeled during conceptual design using New-tonian flow theory.1,2 This theory assumes that when a particle (traveling in rectilinear motion) strikes thesurface of a body, all of the momentum normal to the surface would be lost and all momentum tangentialto the surface would be conserved as shown in Figure 1. Consequently, the pressure exerted by the fluidon the surface of a body is assumed to be solely originating from this loss of momentum normal to thesurface. Under these assumptions, the nondimensional pressure coefficient, Cp, at any point on the surfaceof a body can be obtained from the Newtonian sine-squared relation shown in Eq. (1). Furthermore, thepressure exerted by the fluid on any portion of the surface not directly exposed to the flow, denoted as theshadowed region of the body, is assumed to be equivalent to the freestream pressure in which the motionof the fluid does not influence the pressure in this region. Consequently, Cp = 0 throughout the shadowedregion as shown in Figure 2.

Cp =p p12V

2

= 2 sin2 (1)

Figure 1. Momentum transfer of particle on inclined sur-face.2 Figure 2. Example of shadowed body.

2

The pressure that results from this momentum transfer is integrated over the unshadowed surface of thevehicle to calculate the hypersonic force coefficients as shown in Eq. (2), where n is the unit normal anddf is calculated from Eq. (3). In traditional conceptual design, this surface integration is approximatednumerically in the form of panel methods such as those included within the Configuration Based Aerody-namics (CBAERO) tool3 and the Aerodynamic Preliminary Analysis System (APAS).4,5, 6 Additionally, theaerodynamics of bodies of revolution have been calculated using ring approximation methods.7,8, 9 Althoughthese conceptual numerical methods allow rapid aerodynamic calculations compared to computational fluiddynamics (CFD), this process must be repeated for any change in shape of the vehicle. Additionally, theresolution of the mesh must be addressed when using numerical methods. For example, the number ofrequired panels to achieve a desired accuracy is generally unknown in the beginning of the meshing process.Consequently, multiple meshes of various resolutions must be evaluated until the convergence of aerodynamiccoefficients is observed. The construction of a mesh for complicated shapes would also likely require modelingin a computer-aided design package. While certain tools such as CBAERO provide built-in routines to meshbodies of revolution, other vehicle shapes must be meshed using external tools such as the GNU TriangulatedSurface Library (GTS).10 These time-consuming issues associated with panel methods limit the number ofvehicle shapes analyzed during conceptual design.CACS

CN

= 1Aref

S

dfT xdfT ydfT z

= 1Aref

S

Cp

ninT xninT ynin

T z

dA (2)df = Cp n dA (3)

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I.A. Motivation for Analytic Hypersonic Aerodynamics

While panel methods would likely be required for the conceptual design of complicated geometries such asthe Space Shuttle Orbiter, X-38, and HL-20, many hypersonic vehicle designs used in previous and currentmission studies are not complex. For example, all previous and currently planned Mars missions have usedblunt sphere-cones. Various human Mars mission studies have used blunt sphere-cones and blunted bicon-ics.11,12,13 The Stardust and Genesis Earth entries also used blunt sphere-cones.14,15 The Apollo and Orioncommand modules both utilized a spherical forebody segment. Many high performance military hypersonicvehicles are slender sphere-cones and slender biconics with minor nose blunting to account for extreme heat-ing environments. Some high performance entry vehicles include blended wedge designs, such as the SHARPL1, that consist of flat plates, conical frustums, and nose blunting through a cylindrical segment.16 Theseexamples represent a subset of missions that implement relatively simple vehicle geometries, and Figure 3illustrates the wide range of applications for these geometries.

Figure 3. Example vehicles with analytic geometries.

The surface geometry of these basic shapes, along with additional complex shapes, can be expressedanalytically. Consequently, the Newtonian surface integration that is traditionally performed numericallyusing panel methods can also be performed analytically. Many of the resulting analytic relations provideexact Newtonian aerodynamic coefficients currently approximated by panel methods. Additionally, the eval-uation of most of the analytic relations is nearly instantaneous. As such, these relations could substitutepanel methods widely used in traditional, segregated conceptual design environments to improve the compu-tational performance of Newtonian aerodynamics calculations. More importantly, however, these relationseliminate the large aerodynamic tables that fundamentally segregate aerodynamics from other analyses dur-ing conceptual design and enable the construction of a unified, mathematical framework to perform rapid,simultaneous hypersonic aerodynamic and trajectory optimization.17,18

I.B. Absence of Analytic Aerodynamics in Present-Day Analyses

The limited analytic relations developed in the 1950s and 1960s have largely been forgotten by the aerospacecommunity in the recent decades. The manual development of analytic relations is time-intensive and requirescomplex integrations to be performed. As a result, the integration process is largely dependent on integraltables and appropriate substitutions, requiring substantial trial-and-error effort that is prohibitive duringconceptual design. Rather, the advent of the digital computer resulted in the widespread adoption of paneland CFD methods over historical relations.7,8, 9, 19,20,21,22,23 This can be observed by the many recent shapedesign studies that employ panel methods.24,25

Recent advances in symbolic manipulations tools, such as Mathematica26 and Maple,27 enable the mod-ern construction of analytic relations for various shapes. These symbolic tools are capable of querying largedatabases of integral tables and substitution techniques, addressing some of the limitations that have his-torically prevented the adoption of analytic methods. Recent research has illustrated that the traditionalNewtonian calculation can be performed analytically for a wide range of basic shapes, including conical frus-tums, spherical segments, cylindrical segments, and flat plates, and this research complements the historicalanalytic relations.28 Many common hypersonic vehicles of interest, including those shown in Figure 3, can

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be constructed through the superposition of these basic shapes. As such, the corresponding aerodynamics ofeach basic shape can also be combined to form analytic relations for vehicles of interest. This analytic aero-dynamic database, that includes the analytic relations derived in this investigation, can be downloaded fromthe following file when viewed in Adobe Acrobat ( )a. The enclosedMatlab routines should be referenced for the contents of the analytic expressions. When developing analyticrelations, each vehicle is parametrized such that the resulting solutions must only be developed once and arevalid across all configurations. This is a major advantage over panel methods that must be executed eachtime the shape of the vehicle changes. However, as the complexity of the shape of the vehicle increases, theanalytic solutions also increase in complexity. For certain complex shapes, no analytic solution has currentlybeen found and is a consequence of the fundamental challenges that exist within the traditional Newtoniancalculation.

II. Fundamental Challenges of Analytic Newtonian Aerodynamics

Figure 4. Side and front view of spherical segmentparametrization.

The most apparent challenge during the integra-tion process is that many simple functions cannot beanalytically integrated. For example, the functionsin(x)/x has no known analytic integral. As vehi-cles of greater complexity are considered, no guaran-tee can be made regarding the existence of a closedform, analytic solution. In the most recent analyticwork,28 simple bodies of revolution are analyzed as anattempt to expand the database to include more com-plex shapes. The surface of these bodies is naturallyparametrized using trigonometric functions of the rev-olution angle. For an example spherical segment thatcould serve as the nose of a sphere-cone vehicle withcone angle c and nose radius rn, the revolution an-gle, , shown in Figure 4 corresponds to the naturalsurface parametrization as described by Eq. (4). As a result, the corresponding shadow boundaries thatdetermine the limits of the analytic integration are functions of inverse trigonometric functions. Thesefunctions, when combined with other polynomial expressions that appear during the integration process,generally result in expressions that cannot be analytically integrated. For certain combinations that are an-alytically integrable, the solutions obtained by symbolic manipulation tools such as Mathematica generallyresult in very lengthy expressions that reduce computational performance.

r = [xr2n x2 cos()

r2n x2 sin()]T (4)

To avoid the complexity of inverse trigonometric functions, bodies of revolution could be parametrizedusing Cartesian coordinates. While this parametrization eliminates the inverse trigonometric functions thatappear in the shadow boundary, alternate inverse trigonometric functions appear from the mapping ofCartesian distances (used to provide integration limits that the describe the surface of the shape) to inversetrigonometric functions during integration. An example of a simple distance calculation that results in aninverse trigonometric function is shown in Eq. (5). A similar phenomenon also exists due to the normalvector normalizations required to calculate the pressure coefficient and direction of force as shown in Eq. (3).As a similar example, the normalization term that appears in Eq. (6) also leads to an inverse trigonometricexpression after integration. In fact, many vehicle configurations suffer from this inverse trigonometriccomplexity due to both of these complications.

1 x2 dx = 12

(x

1 x2 + arcsinx) (5)

1

1 x2dx = arcsinx (6)

aPrior to unzipping the file, the REMOVEME portion of the file extension must be removed.

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aerodynamicsDatabase/.DS_Store

__MACOSX/aerodynamicsDatabase/._.DS_Store

aerodynamicsDatabase/bezierRevolution/f_and_M_1_term_new1.m

function out=f_and_M_1_term_new1(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=(-32*b1x*b1y^2*b2x*pi*cos(a)*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new10(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1y*b2x^2*b2y*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new11(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(32*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new12(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1y^2*b2x^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new13(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(8*b1y*b2x^2*b2y*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new14(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new15(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(8*b1x*b2x*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new16(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(2*b2x^2*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new17(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(32*b1x*b1y^2*b2x*pi*cos(a)*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new18(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(24*b1x^2*b1y*b2y*pi*cos(a)*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new19(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(144*b1x^2*b1y^2*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new2(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(24*b1x^2*b1y*b2y*pi*cos(a)*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new20(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(24*b1x*b1y*b2x*b2y*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new21(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(4*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new22(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(320*b1x^2*b1y^2*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new23(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(256*b1x*b1y^2*b2x*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new24(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(16*b1y^2*b2x^2*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new25(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(224*b1x^2*b1y*b2y*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new26(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(8*b1y*b2x^2*b2y*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new27(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(32*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new28(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(8*b1y^2*b2x^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u2+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u2^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new29(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1y*b2x^2*b2y*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u2+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u2^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new3(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(144*b1x^2*b1y^2*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new30(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(8*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u2+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u2^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new31(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1x*b2x*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u2+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u2^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new32(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(2*b2x^2*b2y^2*pi*cos(a)*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u2+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u2^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new33(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(4*b1x^2*b1y^2*pi*cos(b)^2*((-4*b1x^2+2*b1x*b2x+2*b1y*(-2*b1y+b2y))* atan((-(b1y*b2x)+b1x*b2y)/((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1)))+(-(b1y*b2x)+b1x*b2y)*log(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2))*sin(2*a))/(Aref*(-(b1y*b2x)+b1x*b2y)*(2*b1x-b2x+2*b1y*1i-b2y*1i)*(2*b1x-b2x-2*b1y*1i+b2y*1i));

return


function out=f_and_M_1_term_new34(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(56*b1x^2*b1y^2*pi*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new35(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(40*b1x*b1y^2*b2x*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new36(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(4*b1y^2*b2x^2*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new37(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(32*b1x^2*b1y*b2y*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new38(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(80*b1x*b1y*b2x*b2y*pi*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new39(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(8*b1x*b2x*b2y^2*pi*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new4(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(24*b1x*b1y*b2x*b2y*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new40(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(16*b1x^2*b1y^2*pi*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new41(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(16*b1x*b1y^2*b2x*pi*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new42(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(16*b1x^2*b1y*b2y*pi*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new43(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(16*b1x*b1y*b2x*b2y*pi*cos(b)^2*(48*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*u1+6*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u1^2+8*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u1^3+3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4*u1^4-(12*(32*b1x^10-80*b1x^9*b2x-40*b1x^7*b2x*(8*b1y^2+b2x^2-8*b1y*b2y-3*b2y^2)+80*b1x^8*(2*b1y^2+b2x^2-b1y*b2y-b2y^2)-10*b1x^3*b1y^2*b2x*(32*b1y^4-b2x^4-96*b1y^3*b2y+10*b2x^2*b2y^2-5*b2y^4-20*b1y^2*(b2x^2-3*b2y^2))-5*b1x*b1y^4*b2x*(16*b1y^4+b2x^4-64*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-24*b1y^2*(b2x^2-3*b2y^2)+32*b1y*b2y*(b2x^2-b2y^2))+10*b1x^6*(32*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+16*b1y^2*(b2x^2-b2y^2)+12*b1y*b2y*(-3*b2x^2+b2y^2))-b1x^5*b2x*(480*b1y^4+b2x^4-960*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+160*b1y*b2y*(-b2x^2+b2y^2))+b1y^5*(2*b1y-b2y)*(16*b1y^4+5*b2x^4-32*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4-8*b1y^2*(5*b2x^2-3*b2y^2)+8*b1y*(5*b2x^2*b2y-b2y^3))+5*b1x^4*b1y*(64*b1y^5-96*b1y^4*b2y-40*b1y^2*(3*b2x^2*b2y-b2y^3)-b2y*(5*b2x^4-10*b2x^2*b2y^2+b2y^4)-10*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4))+10*b1x^2*b1y^3*(16*b1y^5-32*b1y^4*b2y+5*b2x^4*b2y-10*b2x^2*b2y^3+b2y^5-16*b1y^3*(b2x^2-b2y^2)+4*b1y^2*b2y*(-3*b2x^2+b2y^2)-5*b1y*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(80*b1x^8-160*b1x^7*b2x-40*b1x^5*b2x*(12*b1y^2+b2x^2-8*b1y*b2y-b2y^2)+40*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-b2y^2)-8*b1x^3*b1y*b2x*(60*b1y^3-80*b1y^2*b2y-5*b2x^2*b2y+20*b1y*b2y^2+3*b2y^3)-8*b1x*b1y^3*b2x*(20*b1y^3-40*b1y^2*b2y+3*b2x^2*b2y-5*b2y^3-5*b1y*(b2x^2-5*b2y^2))+b1y^4*(80*b1y^4+b2x^4-160*b1y^3*b2y-10*b2x^2*b2y^2+5*b2y^4-40*b1y^2*(b2x^2-3*b2y^2)+40*b1y*b2y*(b2x^2-b2y^2))+2*b1x^2*b1y^2*(160*b1y^4-5*b2x^4-240*b1y^3*b2y-80*b1y*b2x^2*b2y+38*b2x^2*b2y^2-5*b2y^4+20*b1y^2*(b2x^2+5*b2y^2))+b1x^4*(480*b1y^4+5*b2x^4-480*b1y^3*b2y-10*b2x^2*b2y^2+b2y^4+40*b1y^2*(5*b2x^2+b2y^2)-40*b1y*(5*b2x^2*b2y-b2y^3)))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^5);

return


function out=f_and_M_1_term_new44(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(4*b1x^2*b1y^2*pi*cos(b)^2*((-4*b1x^2+2*b1x*b2x+2*b1y*(-2*b1y+b2y))* atan((-(b1y*b2x)+b1x*b2y)/((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2)))+(-(b1y*b2x)+b1x*b2y)*log(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2))*sin(2*a))/(Aref*(-(b1y*b2x)+b1x*b2y)*(2*b1x-b2x+2*b1y*1i-b2y*1i)*(2*b1x-b2x-2*b1y*1i+b2y*1i));

return


function out=f_and_M_1_term_new45(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(56*b1x^2*b1y^2*pi*cos(b)^2*((4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2-((4*b1x^4-4*b1x^3*b2x+4*b1x*b1y*b2x*(-b1y+b2y)+b1x^2*(8*b1y^2+b2x^2-4*b1y*b2y-b2y^2)+b1y^2*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2);

return


function out=f_and_M_1_term_new46(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(40*b1x*b1y^2*b2x*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new47(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=+(4*b1y^2*b2x^2*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new48(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(32*b1x^2*b1y*b2y*pi*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(2*a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3);

return


function out=f_and_M_1_term_new49(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(80*b1x*b1y*b2x*b2y*pi*cos(b)^2*(3*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*u2+3*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u2^2+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^3*u2^3-(3*(16*b1x^8-32*b1x^7*b2x-8*b1x^5*b2x*(12*b1y^2+b2x^2-12*b1y*b2y-3*b2y^2)+8*b1x^6*(8*b1y^2+3*b2x^2-4*b1y*b2y-3*b2y^2)-8*b1x*b1y^3*b2x*(4*b1y^3-3*b1y*b2x^2-12*b1y^2*b2y+2*b2x^2*b2y+9*b1y*b2y^2-2*b2y^3)-16*b1x^3*b1y*b2x*(6*b1y^3-b1y*b2x^2-12*b1y^2*b2y-b2x^2*b2y+3*b1y*b2y^2+b2y^3)+b1x^4*(96*b1y^4+b2x^4-96*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4+24*b1y^2*(b2x^2-b2y^2)+24*b1y*b2y*(-3*b2x^2+b2y^2))+b1y^4*(16*b1y^4+b2x^4-32*b1y^3*b2y-6*b2x^2*b2y^2+b2y^4-24*b1y^2*(b2x^2-b2y^2)+8*b1y*(3*b2x^2*b2y-b2y^3))+2*b1x^2*b1y^2*(32*b1y^4-48*b1y^3*b2y-12*b1y^2*(b2x^2-b2y^2)+8*b1y*b2y*(-3*b2x^2+b2y^2)-3*(b2x^4-6*b2x^2*b2y^2+b2y^4)))* atan(((b2x^2+b2y^2)*u2+b1x^2*(-2+4*u2)+b1y^2*(-2+4*u2)+b1x*(b2x-4*b2x*u2)+b1y*(b2y-4*b2y*u2))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+6*(8*b1x^6-12*b1x^5*b2x+b1x*b1y^2*b2x*(-12*b1y^2+b2x^2+16*b1y*b2y-5*b2y^2)+2*b1x^4*(12*b1y^2+3*b2x^2-6*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-b2x^2-4*b1y*b2y+b2y^2)+b1x^3*b2x*(-24*b1y^2-b2x^2+16*b1y*b2y+b2y^2)+b1x^2*b1y*(24*b1y^3-24*b1y^2*b2y-5*b2x^2*b2y+b2y^3+4*b1y*(b2x^2+b2y^2)))*log(4*(b1x^2*(1-2*u2)^2+b1y^2*(1-2*u2)^2+2*b1x*b2x*(1-2*u2)*u2+2*b1y*b2y*(1-2*u2)*u2+(b2x^2+b2y^2)*u2^2)))*sin(2*a))/(3*Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^4);

return


function out=f_and_M_1_term_new5(a,b,b1x,b2x,b1y,b2y,u1,u2,Aref,lref)%#emlout=-(4*b1x^2*b2y^2*pi*cos(a)*cos(b)^2*(4*(2*b1x^2-b1x*b2x+b1y*(2*b1y-b2y))*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)*u1+(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y^2)^2*u1^2-(2*(8*b1x^6-12*b1x^5*b2x-b1x^3*b2x*(24*b1y^2+b2x^2-24*b1y*b2y-3*b2y^2)+6*b1x^4*(4*b1y^2+b2x^2-2*b1y*b2y-b2y^2)+b1y^3*(2*b1y-b2y)*(4*b1y^2-3*b2x^2-4*b1y*b2y+b2y^2)-3*b1x*b1y^2*b2x*(4*b1y^2-b2x^2-8*b1y*b2y+3*b2y^2)+3*b1x^2*b1y*(8*b1y^3-8*b1y^2*b2y-3*b2x^2*b2y+b2y^3))* atan(((b2x^2+b2y^2)*u1+b1x^2*(-2+4*u1)+b1y^2*(-2+4*u1)+b1x*(b2x-4*b2x*u1)+b1y*(b2y-4*b2y*u1))/(-(b1y*b2x)+b1x*b2y)))/(b1y*b2x-b1x*b2y)+(12*b1x^4-12*b1x^3*b2x+4*b1x*b1y*b2x*(-3*b1y+2*b2y)+b1x^2*(24*b1y^2+3*b2x^2-12*b1y*b2y-b2y^2)+b1y^2*(12*b1y^2-b2x^2-12*b1y*b2y+3*b2y^2))*log(4*(b1x^2*(1-2*u1)^2+b1y^2*(1-2*u1)^2+2*b1x*b2x*(1-2*u1)*u1+2*b1y*b2y*(1-2*u1)*u1+(b2x^2+b2y^2)*u1^2)))*sin(a))/(Aref*(4*b1x^2+4*b1y^2-4*b1x*b2x+b2x^2-4*b1y*b2y+b2y

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