Collision with friction; Part A: Newton's hypothesis

This paper deals with collision with friction. In Part A, equations governing a one-point collision of planar, simple nonholonomic systems are generated. Expressions for the normal and tangential impulses, the normal and tangential velocities of separation of the colliding points, and the change of the system mechanical energy are written for three types of collision (i.e., forward sliding, sticking, etc.). These together with Routh's semigraphical method and Coulomb's coefficient of friction are used to show that the algebraic signs of four, newly-defined, configuration-related parameters, not all independent, span five cases of system configuration. For each, the ratio between the tangential and normal components of the velocity of approach, called alpha, determine the type of collision, which once found, allows the evaluation of the associated normal and tangential impulses and ultimately the changes in the motion variables. The analysis of these cases indicates that the calculated mechanical energy may increase if sticking or reverse sliding occur. In Part B, theories based on Poisson's and Stronge's hypotheses are presented with more encouraging results.