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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 2, Pages 179–196
DOI: https://doi.org/10.4213/tmf8334 (Mi tmf8334) 		 
This article is cited in 13 scientific papers (total in 13 papers)

One family of conformally Hamiltonian systems

A. V. Tsiganov

Saint-Petersburg State University, Saint-Petersburg, Russia
Full-text PDF (486 kB) Citations (13)
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DOI: https://doi.org/10.4213/tmf8334
Abstract: We propose a method for constructing conformally Hamiltonian systems of dynamical equations whose invariant measure arises from the Hamiltonian equations of motion after a change of variables including a change of time. As an example, we consider the Chaplygin problem of the rolling ball and the Veselova system on the Lie algebra e∗(3) and prove their complete equivalence.
Keywords: integrable system, nonholonomic system, Chaplygin ball, Veselova system.
Received: 13.03.2012
Revised: 09.04.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 2, Pages 1481–1497
DOI: https://doi.org/10.1007/s11232-012-0128-0
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Tsiganov, “One family of conformally Hamiltonian systems”, TMF, 173:2 (2012), 179–196; Theoret. and Math. Phys., 173:2 (2012), 1481–1497
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8334
  • https://doi.org/10.4213/tmf8334
  • https://www.mathnet.ru/eng/tmf/v173/i2/p179
    • This publication is cited in the following 13 articles:
    1. Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref
    2. Alexey V. Borisov, Andrey V. Tsiganov, “On the Chaplygin Sphere in a Magnetic Field”, Regul. Chaotic Dyn., 24:6 (2019), 739–754  mathnet  crossref  mathscinet
    3. Andrey V. Tsiganov, “Bäcklund Transformations for the Nonholonomic Veselova System”, Regul. Chaotic Dyn., 22:2 (2017), 163–179  mathnet  crossref
    4. Andrey V. Tsiganov, “Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball”, Regul. Chaotic Dyn., 22:4 (2017), 353–367  mathnet  crossref
    5. Yury A. Grigoryev, Alexey P. Sozonov, Andrey V. Tsiganov, “Integrability of Nonholonomic Heisenberg Type Systems”, SIGMA, 12 (2016), 112, 14 pp.  mathnet  crossref
    6. Andrey V. Tsiganov, “On Integrable Perturbations of Some Nonholonomic Systems”, SIGMA, 11 (2015), 085, 19 pp.  mathnet  crossref
    7. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. O. E. Fernandez, A. M. Bloch, D. V. Zenkov, “The geometry and integrability of the Suslov problem”, J. Math. Phys., 55:11 (2014), 112704  crossref  mathscinet  zmath  adsnasa  isi
    9. Andrey V. Tsiganov, “On the Lie Integrability Theorem for the Chaplygin Ball”, Regul. Chaotic Dyn., 19:2 (2014), 185–197  mathnet  crossref  mathscinet  zmath
    10. Andrey Tsiganov, “Poisson structures for two nonholonomic systems with partially reduced symmetries”, Journal of Geometric Mechanics, 6:3 (2014), 417  crossref
    11. I. A. Bizyaev, A. V. Tsiganov, “On the Routh sphere problem”, J. Phys. A-Math. Theor., 46:8 (2013), 085202  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640  mathnet
    13. A. V. Tsiganov, “On generalized nonholonomic Chaplygin sphere problem”, Int. J. Geom. Methods Mod. Phys., 10:6 (2013), 1320008  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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