On a Novel Hamiltonian Description of the Nonholonomic Suslov Problem

We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank-four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets of the five-dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank-two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.