Non-integrability of the generalised spring-pendulum problem

Details Non-integrability of the generalised spring-pendulum problem Non-integrability of the generalised spring-pendulum problem

2003-08-08

arxiv.org/abs/math-ph/0308011v1

J. Phys. A, Math. Gen., 2004, vol.37, no. 7, pp. 2579--2597

Physics

Mathematical Physics

20 pages, 1 figure

Scientific paper

10.1023/B:CELE.0000034513.45950.

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 $k\neq -a$. 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.

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