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Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The Wilberforce spring-pendulum

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  • In this paper we analyze the non-integrability of the Wilbeforce spring-pendulum by means of Morales-Ramis theory in where is enough to prove that the Galois group of the variational equation is not virtually abelian. We obtain these non-integrability results due to the algebrization of the variational equation falls into a Heun differential equation with four singularities and then we apply Kovacic's algorithm to determine its non-integrability.
    Mathematics Subject Classification: Primary: 37J30; Secondary: 12H05 34M45 37J35 70G55 70H06.


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