Differential Galois Approach to the Non-integrability of the Heavy Top Problem

Details Differential Galois Approach to the Non-integrability of the Heavy Top Problem Differential Galois Approach to the Non-integrability of the Heavy Top Problem

2004-04-20

arxiv.org/abs/math/0404367v1

Ann. Fac. Sci. Toulouse Math. (6), 2005, vol.14, no.1, pp.123--160

Mathematics

Dynamical Systems

31 pages, 1 figure

Scientific paper

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).

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