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

2011/04/02 by Acosta-Humánez, Primitivo B., Alvarez--Ramírez, Martha, Blázquez-Sanz, David +1
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1104.0312

Abstract

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.

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