Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 012, 19 pages      arXiv:1510.00181
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

The Hojman Construction and Hamiltonization of Nonholonomic Systems

Ivan A. Bizyaev ab, Alexey V. Borisov ac and Ivan S. Mamaev a
a) Udmurt State University, 1 Universitetskaya Str., Izhevsk, 426034 Russia
b) St. Petersburg State University, 1 Ulyanovskaya Str., St. Petersburg, 198504 Russia
c) National Research Nuclear University MEPhI, 31 Kashirskoe highway, Moscow, 115409 Russia

Received October 05, 2015, in final form January 26, 2016; Published online January 30, 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.

Key words: Hamiltonization; Poisson bracket; Casimir functions; invariant measure; nonholonomic hinge; Suslov problem; Chaplygin sleigh.

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