The Hojman Construction and Hamiltonization of Nonholonomic Systems

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• ISSN: 1815-0659
• Main Authors: Bizyaev, I.A., Borisov, A.V., Mamaev, I.S.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147435
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Hojman Construction and Hamiltonization of Nonholonomic Systems / I.A. Bizyaev, A.V. Borisov, I.S. Mamaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ.

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.