Non-integrability of the generalised spring-pendulum problem
نویسندگان
چکیده
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 proving the non-integrability in this case. PACS numbers: 05.45.-a,02.30.Hq,45.20Jj Submitted to: J. Phys. A: Math. Gen. E-mail: [email protected], [email protected], [email protected] Non-integrability of the generalised spring-pendulum problem 2
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