The Poisson Equations in the Nonholonomic Suslov Problem: Integrability, Meromorphic and Hypergeometric Solutions

We consider the Poisson equations for the classical Suslov system of rigid body mechanics and show that under some minor conditions, these equations are solvable in terms of the generalized hypergeometric functions. Using this property we have calculated the angle between the axes of asymptotic rotations of the body and have shown that it does not depend on the initial conditions. Moreover, we also show, that if the equations possess the Painleve property, then, under an extra condition, they admit an additional polynomial first integral, which can be calculated explicitly.