%0 Journal Article %T Kowalevski's Analysis of the Swinging Atwood's Machine. %+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE) %+ Laboratoire de Physique Théorique et Astroparticules (LPTA) %A Babelon, Olivier %A Talon, Michel %A Capdequi-Peyranere, Michel %< avec comité de lecture %Z 09-069 %@ 1751-8113 %J Journal of Physics A: Mathematical and Theoretical %I IOP Publishing %V 43 %N 8 %P 085207 %8 2010-02-05 %D 2010 %Z 0909.5574 %R 10.1088/1751-8113/43/8/085207 %K Systèmes dynamiques %K Intégrabilité %K Critère de Kowalevski-Painlevé %Z PACS: 45.20.Jj , 07.10.-h/ MSC: 70H03, 70H20, 70H33 %Z Physics [physics]/Mathematical Physics [math-ph] %Z Physics [physics]/High Energy Physics - Theory [hep-th]Journal articles %X 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. %G English %2 https://hal.science/hal-00420854v1/document %2 https://hal.science/hal-00420854v1/file/atwood.pdf %L hal-00420854 %U https://hal.science/hal-00420854 %~ IN2P3 %~ UNIV-PARIS7 %~ UPMC %~ LPTA %~ CNRS %~ LPTHE %~ UNIV-MONTP2 %~ TDS-MACS %~ UPMC_POLE_2 %~ UNIV-MONTPELLIER %~ SORBONNE-UNIVERSITE %~ SU-SCIENCES %~ UNIV-PARIS %~ SU-TI %~ ALLIANCE-SU %~ UM1-UM2