Differential Galois Approach to the Non-integrability of the Heavy Top Problem
Dynamical Systems
2007-05-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We study integrability of the Euler-Poisson equations describing the motion of a rigid body with one fixed point in a constant gravity field. Using the Morales-Ramis theory and tools of differential algebra we prove that a symmetric heavy top is integrable only in the classical cases of Euler, Lagrange, and Kovalevskaya and is partially integrable only in the Goryachev-Chaplygin case. Our proof is alternative to that given by Ziglin ({\em Funktsional. Anal. i Prilozhen.}, 17(1):8--23, 1983; {\em Funktsional. Anal. i Prilozhen.}, 31(1):3--11, 95, 1997).
Keywords
Cite
@article{arxiv.math/0404367,
title = {Differential Galois Approach to the Non-integrability of the Heavy Top Problem},
author = {Andrzej J. Maciejewski and Maria Przybylska},
journal= {arXiv preprint arXiv:math/0404367},
year = {2007}
}
Comments
31 pages, 1 figure