Abstract
A variety of situations is described in which two gliders ride on an “air track” and undergo collisions with each other and with reflecting springs at the ends of the track. In many cases the observed sequence of events has a regular and repetitive behavior, in which the initial conditions are restored after a long sequence of collisions. A general matrix formalism is established for the description of such sequences of collisions, and it is shown that in many cases, the regularities can be easily understood in terms of the properties of the collision matrices, independent of the mass ratio of the gliders. A class of sequences in which the mass ratio is of critical importance is suggested by the formalism and experimentally confirmed. An equivalent geometrical description is given in which a sequence of collisions can be described as simply a succession of rotations and reflections, without change of length, of a “velocity vector” in “velocity space.”
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