Kowalevski's analysis of the swinging Atwood's machine
O Babelon, M Talon, M Capdequi Peyranère · Journal of Physics A Mathematical and Theoretical · 2010
We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is an 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 Painlevé type. However, in view of these expansions, it is not possible to distinguish between integrable and nonintegrable cases.