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

SIGMA 12 (2016), 112, 14 pages      arXiv:1603.03528

Integrability of Nonholonomic Heisenberg Type Systems

Yury A. Grigoryev a, Alexey P. Sozonov a and Andrey V. Tsiganov ab
a) St. Petersburg State University, St. Petersburg, Russia
b) Udmurt State University, Izhevsk, Russia

Received March 17, 2016, in final form November 22, 2016; Published online November 25, 2016

We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical $r$-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.

Key words: Hamiltonian dynamics; nonholonomic systems.

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