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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 012, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.012 (Mi sigma1094) 		 
This article is cited in 11 scientific papers (total in 11 papers)

The Hojman Construction and Hamiltonization of Nonholonomic Systems

Ivan A. Bizyaevab, Alexey V. Borisovac, Ivan S. Mamaeva

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
Full-text PDF (628 kB) Citations (11)
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DOI: https://doi.org/10.3842/SIGMA.2016.012
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 15-12-20035
Russian Foundation for Basic Research 15-31-50172
Ministry of Education and Science of the Russian Federation
Section 3 was prepared by A.V. Borisov under the RSF grant No. 15-12-20035. Section 2 was written by I.S. Mamaev within the framework of the state assignment for institutions of higher education. The work of I.A. Bizyaev (Sections 4 and 5) was supported by RFBR grant No. 15-31-50172.
Received: October 5, 2015; in final form January 26, 2016; Published online January 30, 2016
Bibliographic databases:
Document Type: Article
MSC: 37J60; 37J05
Language: English
Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hojman Construction and Hamiltonization of Nonholonomic Systems”, SIGMA, 12 (2016), 012, 19 pp.
Citation in format AMSBIB
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\by Ivan~A.~Bizyaev, Alexey~V.~Borisov, Ivan~S.~Mamaev
\paper The Hojman Construction and Hamiltonization of Nonholonomic Systems
\jour SIGMA
\yr 2016
\vol 12
\papernumber 012
\totalpages 19
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\crossref{https://doi.org/10.3842/SIGMA.2016.012}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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