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Polynomial integrals of reversible mechanical systems with a two-dimensional torus as the configuration space. (English. Russian original) Zbl 0964.70015
Sb. Math. 191, No. 2, 189-208 (2000); translation from Mat. Sb. 191, No. 2, 43-63 (2000).
The authors consider natural mechanical systems that have a two-dimensional torus as the configuration space and admit an additional first integral which is polynomial with respect to momenta. It is shown that the systems of this type are completely integrable, and their polynomial integrals can be represented as sums of homogeneous polynomials in momenta with coefficients that are smooth single-valued functions on the configuration space.

MSC:
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
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