Resolving Kane's Puzzle in Oblique Collisions of Rigid Bodies

Abstract

We examined the asymmetric deformation in collisions and the transition conditions from oblique to normal collisions and non-collisions to address the problem of oblique collisions of rigid bodies in classical mechanics. A closed solution satisfying the fundamental equations and adhering to the energy conservation law without introducing new material parameters was derived. The solution exhibited a nonlinear relationship between post-collision velocity and initial state parameters, contrasting with the linear results of existing studies. This solution avoided the fallacy in Whittaker's hypothesis that kinetic energy might increase after a collision. Consequently, the solution presented herein fundamentally resolves Kane's puzzle, previously overlooked in classical mechanics.