The Gauss-Knörrer map for the Rosochatius dynamical system.(English)Zbl 0984.37066

Summary: We found a nonlinear integrable system dual to the Rosochatius dynamical system in arbitrary dimensions by means of the Gauss-Knörrer map. The relationship between the Rosochatius system and its dual system is elucidated from the point of view of constrained Hamiltonian systems. Dirac brackets for dynamical variables and conserved quantities for the dual system are derived explicitly.

MSC:

 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 70H05 Hamilton’s equations 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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