Abstract:
We discuss, in all generality, the reduction of the Hamilton – Jacobi equation for systems subject to nonholonomic constraints and invariant under the action of a group of symmetries.We consider nonholonomic systems subject to both linear and nonlinear constraints and with different positioning of such constraints with respect to the symmetries.
Keywords:
Hamilton – Jacobi, theory of reduction, nonholonomic systems; constrained systems, nonlinear constraints, reconstruction, symplectic reduction, Marsden –Weinstein reduction, symmetries.
This work has been partially supported by MINECO Grants MTM2016-76-072-P and the
ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554. V.M. Jiménez wishes to thank
MINECO for a FPI-PhD position.
Citation:
Ogul Esen, Victor M. Jiménez, Manuel de León, Cristina Sardón, “Reduction of a Hamilton – Jacobi Equation for Nonholonomic Systems”, Regul. Chaotic Dyn., 24:5 (2019), 525–559
\Bibitem{EseJimDe 19}
\by Ogul Esen, Victor M. Jim\'enez, Manuel de Le\'on, Cristina Sard\'on
\paper Reduction of a Hamilton – Jacobi Equation for Nonholonomic Systems
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 5
\pages 525--559
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https://www.mathnet.ru/eng/rcd1025
https://www.mathnet.ru/eng/rcd/v24/i5/p525
This publication is cited in the following 3 articles:
José F. Cariñena, Partha Guha, “Lichnerowicz-Witten Differential, Symmetries and Locally Conformal Symplectic Structures”, Journal of Geometry and Physics, 2025, 105418
Oğul Esen, Miroslav Grmela, Michal Pavelka, “On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective”, Journal of Mathematical Physics, 63:12 (2022)
O Esen, M de León, M Lainz, C Sardón, M Zając, “Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities”, J. Phys. A: Math. Theor., 55:40 (2022), 403001
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