Numerical evidence of nonintegrability of certain Lie-Poisson system

We consider a system of differential equations describing the rotational motion of a rigid body whose center of mass moves in a circular orbit. The aim is to prove its nonintegrability. For this purpose we apply Ziglin theorem about nonintegrability of Hamiltonian systems. In the system studied the assumptions of this theorem can be checked numerically. We describe a numerical technique adequate for this purpose. Using it we obtain a ‘numerical proof’ that, the system is not integrable.