Stronge’s hypothesis-based solution to the planar collision-with-friction problem

Abstract

Listen

Translate article

This paper deals with collision with friction. Differential equations governing a one-point collision of planar, simple non-holonomic systems are generated. Expressions for quantities of interest (e.g., normal and tangential impulses, normal and tangential relative velocities of the colliding points, and the change of the system mechanical energy), are written for five types of collision (i.e., sticking in compression, forward sliding, etc.) associated with Stronge’s collision hypothesis and Coulomb’s coefficient of friction, in conjunction with a two-integration procedure. These expressions, together with Routh’s semi-graphical method are used to show that the algebraic signs of four configuration-related parameters span five cases of system configuration. For each, the ratio between the tangential and normal components of the velocity of approach, called α, determine the type of collision which, once found, allows the evaluation of the changes in the motion variables. The analysis of these cases indicates that an algebraic, Stronge’s hypothesis-based solution to the planar collision-with-friction problem always exists, and is unique, coherent and energy consistent. Finally, substitutions are found which transform the Stronge’s hypothesis-based solution to a Poisson’s hypothesis-based and to a Newton’s hypothesis-based solutions appearing in the literature.