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).
Categories: math.DS math-ph math.MP nlin.SI