Non-integrability of the generalised spring-pendulum problem

Abstract

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 $k\ne -a$. 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 proving the non-integrability in this case.

20 pages, 1 figure

References in corpus (1)

• Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields

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