A new approach in the study of frictionless collisions using inertances

Abstract

This paper presents a complete study on the collision without friction of two rigid bodies with and without bilateral constraints. Our goal is to obtain the same formulae for the impulse, the energy of the lost velocities, and the loss of kinetic energy as in the case of the collision of two particles. The study is performed with the aid of the notion of inertance. The dependence on the constraints is given by the inertances. The calculations are realized using the results from the theory of screws (plückerian coordinates). The obtained formulae are general, written in matrix form, and they may be easily used in any practical problem. We give the general algorithms for the collision of two rigid bodies with and without bilateral constraints. The equality of the coefficients of restitution in the Newton, Poisson, and energetic models is also proved. The numerical examples highlight the theory.