The harmony in the Kepler and related problems | Zendy

M. C. Nucci | Zendy; P. G. L. Leach | Zendy

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The harmony in the Kepler and related problems

Author(s) -

M. C. Nucci,

P. G. L. Leach

Publication year - 2001

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1337614

Subject(s) - homogeneous space , kepler problem , harmonic oscillator , kepler , symmetry group , simple harmonic motion , mathematics , theoretical physics , physics , classical mechanics , quantum mechanics , planet , geometry , astronomy

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 tothose reported by Krause ({\it J Math Phys} {\bf 35} (1994) 5734-5748) in hisstudy of the complete symmetry group of the Kepler Problem. The technique isshown to be applicable to related problems containing a drag term which havebeen used to model the motion of low altitude satellites in the Earth'satmosphere and further generalisations. A consequence of the application ofthis technique is the demonstration of the group theoretical relationshipbetween the simple harmonic oscillator and the Kepler and related problems

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