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On Integrable Perturbations of Some Nonholonomic Systems
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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On Integrable Perturbations of Some Nonholonomic Systems
Інший ID:
2010 Mathematics Subject Classification: 37J60; 70G45; 70H45
DOI:10.3842/SIGMA.2015.085
DOI:10.3842/SIGMA.2015.085
Посилання:
On Integrable Perturbations of Some Nonholonomic Systems / A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
We are greatly indebted B. Jovanovi´c and the anonymous referees for a relevant contribution
to improve the paper. The work on the revised, final version of this paper was supported by
Russian Science Foundation (project No 15-12-20035).
Дата:
2015
Переглядів:
470
Завантажень:
233
Анотація:
Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and Heisenberg problems are discussed in the framework of the classical Bertrand-Darboux method. We study the relations between the Bertrand-Darboux type equations, well studied in the holonomic case, with their nonholonomic counterparts and apply the results to the construction of nonholonomic integrable potentials from the known potentials in the holonomic case.
