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Non-integrability of the generalised spring-pendulum problem

Andrzej J. Maciejewski·Maria Przybylska·Jacques-Arthur Weil
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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 $k\neq -a$. 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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Andrzej J. Maciejewski, Maria Przybylska, Jacques-Arthur Weil. 2003-08-08. Non-integrability of the generalised spring-pendulum problem. https://doi.org/10.1023/b%3Acele.0000034513.45950.86

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