Non-integrability of the degenerate cases of the Swinging Atwood'sMachine using higher order variational equations

Regina Martínez; Carles Simó

doi:10.3934/dcds.2011.29.1

Article Contents

2011, Volume 29, Issue 1: 1-24. Doi: 10.3934/dcds.2011.29.1

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Non-integrability of the degenerate cases of the Swinging Atwood's Machine using higher order variational equations

Regina Martínez^1, and
Carles Simó^2,

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona
2.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona

Received: December 31, 2009

Revised: June 30, 2010

Published: December 2010

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Abstract

Non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations (VE_k), are applied to prove the non-integrability of the Swinging Atwood's Machine for values of the parameter which can not be decided using first order variational equations (VE₁).

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Mathematics Subject Classification: Primary: 37J30, 70H07; Secondary: 34M35.

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