0 30 80 11 v 1 8 A ug 2 00 3 Non-integrability of the generalised spring-pendulum problem

  title={0 30 80 11 v 1 8 A ug 2 00 3 Non-integrability of the generalised spring-pendulum problem},
  author={Andrzej J. Maciejewski and Maria Przybylska and Jacques-Arthur Weil},
We investigate a generalisation of the three dimensional spring-pendulum system. The problem depends on two real parameters (k, a), where k is the Young modulus of the spring and a describes the nonlinearity of elastic forces. We show that this system is not integrable when k 6= −a. We carefully investigated the case k = −a when the necessary condition for integrability given by the Morales-Ramis theory is satisfied. We discuss an application of the higher order variational equations for… CONTINUE READING

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