Suslov problem with the Klebsh-Tisserand potential

In this paper, we study a nonholonomic mechanical system, namely the Suslov problem with the Klebsh-Tisserand potential. We analyze the topology of the level sets defined by the integrals in two ways: using an explicit construction and as a consequence of the Poincar'e-Hopf theorem. We describe the flow on such manifolds.