Numerical evidence of nonintegrability of certain Lie-Poisson system

We consider a system of differential equations describing the rotational mo tion of a rigid body whose center of mass moves in a circular orbit. The ai m is to prove its nonintegrability. For this purpose we apply Ziglin theore m about nonintegrability of Hamiltonian systems. In the system studied the assumptions of this theorem can be checked numerically. We describe a numer ical technique adequate for this purpose. Using it we obtain a 'numerical p roof' that the system is not integrable.