The harmony in the Kepler and related problems

Details The harmony in the Kepler and related problems The harmony in the Kepler and related problems

2000-11-06

arxiv.org/abs/nlin/0011011v1

J. Math. Phys. 42 (2001) 746-764

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1063/1.1337614

The technique of reduction of order developed by Nucci ({\it J Math Phys} {\bf 37} (1996) 1772-1775) is used to produce nonlocal symmetries additional to those reported by Krause ({\it J Math Phys} {\bf 35} (1994) 5734-5748) in his study of the complete symmetry group of the Kepler Problem. The technique is shown to be applicable to related problems containing a drag term which have been used to model the motion of low altitude satellites in the Earth's atmosphere and further generalisations. A consequence of the application of this technique is the demonstration of the group theoretical relationship between the simple harmonic oscillator and the Kepler and related problems.

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