Non-integrability Criterium for Normal Variational Equations around an integrable Subsystem and an example: The Wilbeforce spring-pendulum
Dynamical Systems
2012-02-29 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1104.0312,
title = {Non-integrability Criterium for Normal Variational Equations around an integrable Subsystem and an example: The Wilbeforce spring-pendulum},
author = {Primitivo B. Acosta-Humánez and Martha Alvarez--Ramírez and David Blázquez-Sanz and Joaquín Delgado},
journal= {arXiv preprint arXiv:1104.0312},
year = {2012}
}
Comments
23 pages, 1 figure. Keywords and Phrases. Algebrization, Kovacic's algorithm, Hamiltonian systems, Wilbeforce pendulum, Differential Galois Group