Abstract

We present a complete and elegant mathematical description of the sequence of linear collisions between two particles followed by reflection on a wall. The velocities of the particles can be obtained, at any stage of the sequence, in a direct manner. This feature of our solution allows us a priori to find, as a function of the mass ratio, the total number of collisions of each sequence. We also calculate the special ratios which make the final situation a simple reflection of the initial one.

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