%0 Journal Article %T The Hojman construction and Hamiltonization of nonholonomic systems %A Ivan A. Bizyaev %A Alexey V. Borisov %A Ivan S. Mamaev %J Physics %D 2015 %I arXiv %X 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 are degenerate, and for them an invariant measure and Casimir functions can be globally absent in the general case. %U http://arxiv.org/abs/1510.00181v3