The Hojman Construction and Hamiltonization of Nonholonomic Systems - Bizyaev, I.A.; Borisov, A.V.; Mamaev, I.S. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.