# American Institute of Mathematical Sciences

March  2013, 33(3): 965-986. doi: 10.3934/dcds.2013.33.965

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

 1 Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla, Colombia 2 Departamento de Matemáticas, UAM-Iztapalapa, 09340 Iztapalapa, México, D.F., Mexico 3 Universidad Sergio Arboleda, Calle 74 no. 14-14, Bogotá, D.C. 4 Departamento de Matemáticas, Universidad Autónoma Metropolitana – Iztapalapa, 09340 Iztapalapa, México, D. F.

Received  April 2011 Revised  March 2012 Published  October 2012

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.
Citation: Primitivo B. Acosta-Humánez, Martha Alvarez-Ramírez, David Blázquez-Sanz, Joaquín Delgado. Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The Wilberforce spring-pendulum. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 965-986. doi: 10.3934/dcds.2013.33.965
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##### References:
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