1104.0312 (Primitivo B. Acosta-Humánez et al.)

Non-integrability Criterium for Normal Variational Equations around an
integrable Subsystem and an example: The Wilbeforce spring-pendulum    [PDF]

Primitivo B. Acosta-Humánez, Martha Alvarez--Ramírez, David Blázquez-Sanz, Joaquín Delgado

In this paper we analyze the non-integrability of the Wilbeforce 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.

View original: http://arxiv.org/abs/1104.0312