Impulse response

LOGO

Impulse response, analytical methods

DynamicsIqbal Ali Husni

LOGO

Hamiltonian approach

LOGO

Hamiltonian approach

(2.311)

LOGO

Legrangian approach

(2.313)

(2.314)

(2.315)

LOGO

Constrained impulsive motion

(2.318)

(2.320)

LOGO


Finally we can write the general equation for constrained impulsive motion

(2.321)

(2.323)

LOGO

Legrangian multiplier form

LOGO

Impulsive Constraints

(2.329)

LOGO

Example 2.13

The values of coordinates are

The corresponding velocities

just before impact are

LOGO


Three holonomic constraints which specify the particle separation are

Upon differentiation w.r.t time, these equation take form

These equations are valid continuously before and after the impact

LOGO


LOGO


LOGO

Energy relations

LOGO

Energy relations

LOGO

Impulsive constraints

LOGO


LOGO


LOGO


LOGO

Example 2.14

LOGO

Example 2.14

LOGO


LOGO


(2.388)

(2.389)

(2.390)

(2.392)

(2.391)

LOGO

Education

Impulse response