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).