62 articles – 636 references  [version française]
HAL: hal-00420854, version 1

Detailed view  Export this paper
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
(2010-02-05)

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
Fulltext link: 
http://fr.arXiv.org/abs/0909.5574
Attached file list to this document: 
PDF
atwood.pdf(471.3 KB)
PS
atwood.ps(758.3 KB)