On multiple impact
The problem of collision between material rigid objects is of historical as well as practical importance. The relationships, paradoxes and challenges in the study of multiple impacts form the contents of the present paper. The author discusses the following topics: methods for solving the multiple-impact problems, collision of three spheres, three-dimensional collision between three balls, collision of three bodies of arbitrary shape, collision between many bodies, and collision of constrained bodies. In each part suitable examples are presented for detailed analysis. In the final section the author provides detailed conclusions arrived at as a result of earlier studies on particular problems. Three kinds of multiple impacts are addressed depending on the configuration of the systems and the dynamical properties of the colliding bodies: regular type, stochastic type, and quasi-level type. The author obtains regularity criteria for a collision between three or more free bodies and for the impact of a physical pendulum against an obstacle.
collision of three bodies of arbitrary shape
scientific article; zbMATH DE number 1077520