# Kowalevski's Analysis of the Swinging Atwood's Machine.

Abstract : 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 Painlevé type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.
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Journal articles
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (8), pp.085207. <10.1088/1751-8113/43/8/085207>
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https://hal.archives-ouvertes.fr/hal-00420854
Contributor : Michel Talon <>
Submitted on : Tuesday, September 29, 2009 - 6:30:41 PM
Last modification on : Tuesday, October 11, 2016 - 1:25:29 PM
Document(s) archivé(s) le : Wednesday, June 16, 2010 - 12:13:05 AM

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### Citation

Olivier Babelon, Michel Talon, Michel Capdequi-Peyranere. Kowalevski's Analysis of the Swinging Atwood's Machine.. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (8), pp.085207. <10.1088/1751-8113/43/8/085207>. <hal-00420854>

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