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Manev problem and its real form dynamics: superintegrability and symmetry algebras. (English) Zbl 1105.37053
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 203-217 (2006).
The authors show that the Manev model possesses Ermano-Bernoulli-type invariants and symmetry algebras su(2)so(3) or so(2,1) in addition to the angular momentum algebra. These two facts indicate that the Manev model provides better description of the real motion of the heavenly bodies than the Kepler model and in the same times, it shares its most celebrated mathematical features: its superintegrability and large symmetry algebras.
MSC:
37N05Dynamical systems in classical and celestial mechanics
70F05Two-body problems
70G65Symmetries, Lie-group and Lie-algebra methods for dynamical systems
37J35Completely integrable systems, topological structure of phase space, integration methods
37J15Symmetries, invariants, invariant manifolds, momentum maps, reduction