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A problem in classical mechanics

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Abstract

The paper examines the problem concerning the maximum number of times N identical particles can collide elastically with each other in three-dimensional space. The one-dimensional problem is solved and the results are generalized for the case of three different masses. An upper bound for collisions in one dimension is obtained. One advantage of the obtained theorems is that they do not use the detailed dynamics of the particles; if these theorems could be generalized to four or more point particles, the results would be significant.

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