Collision with friction; Part B: Poisson's and Stornge's hypotheses

In Part B of this paper, planar collision theories, counterparts of the theory associated with Newton's hypotheses described in Part A, are developed in connection with Poisson's and Stronge's hypotheses. First, expressions for the normal and tangential impulses, the normal and tangential velocities of separation, and the change of the system mechanical energy are written for five types of collision. These together with Routh's semigraphical method and Coulomb's coefficient of friction are used to show that the algebraic signs of the four parameters introduced in Part A span the same five cases of system configuration of Part A. For each, alpha determines the type of collision which once found allows the evaluation of the normal and tangential impulses and ultimately the changes in the motion variables. The analysis of the indicated cases shows that for Poisson's hypothesis, a solution always exists which is unique, coherent and energy-consistent. The same applies to Stronge's hypothesis, however, for a narrower range of application. It is thus concluded that Poisson's hypothesis is superior as compared with Newton's and Stronge's hypotheses.