Geodesic
The Hojman Construction and Hamiltonization of Nonholonomic Systems
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016)

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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.
Keywords: Hamiltonization; Poisson bracket; Casimir functions; invariant measure; nonholonomic hinge; Suslov problem; Chaplygin sleigh. 
Ivan A. Bizyaev; Alexey V. Borisov; Ivan S. Mamaev. The Hojman Construction and Hamiltonization of Nonholonomic Systems. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a11/
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