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

AUTHORS: 
R. Martinez
Dept. de Matematiques, Univ. Autonoma de Barcelona
Barcelona, Catalunya, Spain 
E-mail:reginamb@mat.uab.cat

C. Simo
Dept. de Matematica Aplicada i Analisi, Univ. de Barcelona
Barcelona, Catalunya, Spain
E-mail:carles@maia.ub.es

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 (VE_1).

Preprint submitted to Discrete and Continuous Dynamical Systems, A, April 2009.

Published in Discrete and Continuous Dynamical Systems, A, 29 (2011) 1-24