A new approach in the study of the collisions with friction using inertances

This paper presents a complete study on the collision with friction of one or two rigid bodies without constraints. The differential formula between the velocities and impulse uses the notion of inertance resulting from the theory of screws (Plückerian coordinates). One thus may calculate the kinematic and dynamic parameters, the velocities and the kinetic energies of the two rigid solids after the collision, and the variation of the kinetic energy. The calculation is detailed for the Newton, Poisson, and energetic variants of the coefficient of restitution. The variation of the kinematic and dynamic parameters in relation to the coefficient of restitution and coefficient of friction for all the three variants are presented and discussed. A numerical example highlights the theory.