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Integrable model of a two-dimensional singular spherical oscillator in a constant magnetic field. (English. Russian original) Zbl 1227.70020

Theor. Math. Phys. 156, No. 1, 1075-1080 (2008); translation from Teor. Mat. Fiz. 156, No. 1, 131-137 (2008).
Summary: We propose an analogue of a two-dimensional singular oscillator (Smorodinsky-Winternitz oscillator) on a sphere, which is exactly solvable in the classical sense both without and with a constant magnetic field. We find explicit classical solutions.

MSC:

70K99 Nonlinear dynamics in mechanics
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
78A99 General topics in optics and electromagnetic theory
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