Coisotropic quasi-periodic motions for a constrained system of rigid bodies

Abstract

We consider a constrained system of four rigid bodies located in axisymmetric potential and gyroscopic force fields and interacting by means of angular velocities. We describe an integrable case (not in Liouville sence!) when 12-dimensional phase space of the above system is fibered by the coisotropic invariant tori, the majority of which carry quasi-periodic motions with 7 independent frequences.