English

The harmony in the Kepler and related problems

Exactly Solvable and Integrable Systems 2009-10-31 v1 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.nlin/0011011,
  title  = {The harmony in the Kepler and related problems},
  author = {M. C. Nucci and P. G. L. Leach},
  journal= {arXiv preprint arXiv:nlin/0011011},
  year   = {2009}
}
R2 v1 2026-07-22T18:07:29.058Z