Abstract
The case of motion of a generalized two-field gyrostat found by V. V. Sokolov and A.V. Tsiganov is known as a Liouville integrable Hamiltonian system with three degrees of freedom. For this system, we find some special periodic motions at which the momentum mapping has rank 1. For such motions, all phase variables can be expressed in terms of algebraic functions of a single auxiliary variable and a set of constants. This auxiliary variable satisfies a differential equation which can be integrated in elliptic functions of time. As an application, the explicit formulas of characteristic exponents for determining the Williamson type of the special periodic motions are obtained.
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This work is partially supported by the grants of RFBR Nos. 16-01-00170, 16-01-00809, 16-01-00378, 17-01-00846 and the grant of the President of the Russian Federation for State Support of Leading Scientific Schools no. 7962.2016.1.
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Oshemkov, A.A., Ryabov, P.E. & Sokolov, S.V. Explicit determination of certain periodic motions of a generalized two-field gyrostat. Russ. J. Math. Phys. 24, 517–525 (2017). https://doi.org/10.1134/S1061920817040100
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DOI: https://doi.org/10.1134/S1061920817040100