Kowalevski's analysis of the swinging Atwood's machine

Details Kowalevski's analysis of the swinging Atwood's machine Kowalevski's analysis of the swinging Atwood's machine

2009-09-30

arxiv.org/abs/0909.5574v1

Physics

Mathematical Physics

30 pages

Scientific paper

We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so--called weak Painlev\'e type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.

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