Andrzej J.~Maciejewski, Maria Przybylska
Differential Galois Approach to the Non-integrability of the Heavy Top Problem
(315K, postscript)
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 (Funktsional. Anal. i Prilozhen., 17(1):8--23,
1983; Funktsional. Anal. i Prilozhen., 31(1):3--11, 95, 1997).