Abstract:
We revise the solution to the problem of Hamiltonization of the n-dimensional Veselova non-holonomic system studied previously in [1]. Namely, we give a short and direct proof of the hamiltonization theorem and also show the trajectorial equivalence of the problem with the geodesic flow on the ellipsoid.
\Bibitem{FedJov09}
\by Yu. N. Fedorov, B. Jovanovi\'c
\paper Hamiltonization of the generalized Veselova LR system
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 4-5
\pages 495--505
\mathnet{http://mi.mathnet.ru/rcd978}
\crossref{https://doi.org/10.1134/S1560354709040066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2551872}
\zmath{https://zbmath.org/?q=an:1229.37086}
Linking options:
https://www.mathnet.ru/eng/rcd978
https://www.mathnet.ru/eng/rcd/v14/i4/p495
This publication is cited in the following 16 articles:
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Garcia-Naranjo L. U. I. S. C. Vermeeren M. A. T. S., “Structure Preserving Discretization of Time-Reparametrized Hamiltonian Systems With Application to Nonholonomic Mechanics”, J. Comput. Dynam., 8:3 (2021), 241–271
Garcia-Naranjo L.C. Marrero J.C., “the Geometry of Nonholonomic Chaplygin Systems Revisited”, Nonlinearity, 33:3 (2020), 1297–1341
Kurt M. Ehlers, Jair Koiller, “Cartan meets Chaplygin”, Theor. Appl. Mech., 46:1 (2019), 15–46
Luis C. García-Naranjo, “Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere”, Theor. Appl. Mech., 46:1 (2019), 65–88
Fasso F. Garcia-Naranjo L.C. Montaldi J., “Integrability and Dynamics of the N-Dimensional Symmetric Veselova TOP”, J. Nonlinear Sci., 29:3 (2019), 1205–1246
Garcia-Naranjo L.C., “Generalisation of Chaplygin'S Reducing Multiplier Theorem With An Application to Multi-Dimensional Nonholonomic Dynamics”, J. Phys. A-Math. Theor., 52:20 (2019), 205203
A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538
Andrey Tsiganov, “Poisson structures for two nonholonomic systems with partially reduced symmetries”, Journal of Geometric Mechanics, 6:3 (2014), 417
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328
Applications of Contact Geometry and Topology in Physics, 2013, 277
A. V. Tsiganov, “One family of conformally Hamiltonian systems”, Theoret. and Math. Phys., 173:2 (2012), 1481–1497
Manuel de León, “A historical review on nonholomic mechanics”, RACSAM, 106:1 (2012), 191
Tomoki Ohsawa, Oscar E. Fernandez, Anthony M. Bloch, Dmitry V. Zenkov, “Nonholonomic Hamilton–Jacobi theory via Chaplygin Hamiltonization”, Journal of Geometry and Physics, 61:8 (2011), 1263
Božidar Jovanović, “Hamiltonization and Integrability of the Chaplygin Sphere in ℝ n”, J Nonlinear Sci, 20:5 (2010), 569
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