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Journal of Physics A Mathematical and Theoretical 43, 8 (2010) 085207
Kowalevski's Analysis of the Swinging Atwood's Machine.
Olivier Babelon1, Michel Talon1, Michel Capdequi-Peyranere2

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.
1:  LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2:  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physics/Mathematical Physics

Physics/High Energy Physics - Theory
Systèmes dynamiques – Intégrabilité – Critère de Kowalevski-Painlevé
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