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Explicit determination of certain periodic motions of a generalized two-field gyrostat. (English) Zbl 1412.70002
Summary: The case of motion of a generalized two-field gyrostat found by V. V. Sokolov and A. V. Tsyganov 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.
70E05 Motion of the gyroscope
37N05 Dynamical systems in classical and celestial mechanics
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
Full Text: DOI
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