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SIGMA, 2016, Volume 12, 012, 19 pages (Mi sigma1094)  

This article is cited in 6 scientific papers (total in 6 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

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.


DOI: https://doi.org/10.3842/SIGMA.2016.012

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Full text: http://www.emis.de/.../012
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Bibliographic databases:

ArXiv: 1510.00181
MSC: 37J60; 37J05
Received: October 5, 2015; in final form January 26, 2016; Published online January 30, 2016
Language:

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
\mathnet{http://mi.mathnet.ru/sigma1094}
\crossref{https://doi.org/10.3842/SIGMA.2016.012}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Oğul Esen, Anindya Ghose Choudhur, Partha Guha, Hasan Gümral, “Superintegrable Cases of Four-dimensional Dynamical Systems”, Regul. Chaotic Dyn., 21:2 (2016), 175–188  mathnet  crossref  mathscinet
    2. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period”, Regul. Chaotic Dyn., 21:4 (2016), 455–476  mathnet  crossref
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Hamilton's principle and the rolling motion of a symmetric ball”, Dokl. Phys., 62:6 (2017), 314–317  crossref  crossref  mathscinet  isi  elib  elib
    5. I. A. Garcia, B. Hernandez-Bermejo, “Inverse Jacobi multiplier as a link between conservative systems and Poisson structures”, J. Phys. A-Math. Theor., 50:32 (2017), 325204  crossref  mathscinet  zmath  isi
    6. Tsiganov A.V., “Hamiltonization and Separation of Variables For a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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