Dynamics systems with extremely heterogeneous inertia properties
Abstract
The paper investigates the problem arising when, in attempting to integrate the Lagrangian equations of motion, one has to deal with a determinant of the inertia coefficients that is very small. This is likely to occur in systems possessing components whose masses or moments of inertia are very small compared to those of others. A method of dealing with this situation is suggested. Instead of integrating the original equations, one sets disproportionately small masses and moments of inertia equal to zero and considers separately regimes of motion during which the absence of constraints makes it possible to work with readily integrable equations, and regimes for which an analysis based on the assumption of the occurrence of elastic collisions permits the formulation of algebraic relationships governing concomitant sudden changes in velocities and angular velocities.
 Publication:

Mechanics Research Communications
 Pub Date:
 1976
 Bibcode:
 1976MeReC...3..489K
 Keywords:

 Elastodynamics;
 EulerLagrange Equation;
 Moments Of Inertia;
 Pendulums;
 Angular Velocity;
 Elastic Scattering;
 Kinetic Energy;
 Numerical Integration;
 Physics (General)