Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 11 (2015), 085, 19 pages      arXiv:1505.01588      https://doi.org/10.3842/SIGMA.2015.085
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

On Integrable Perturbations of Some Nonholonomic Systems

Andrey V. Tsiganov ab
a) St. Petersburg State University, St. Petersburg, Russia
b) Udmurt State University, 1 Universitetskaya Str., Izhevsk, Russia

Received May 08, 2015, in final form October 16, 2015; Published online October 20, 2015

Abstract
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.

Key words: nonholonomic system; integrable systems.

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