The harmony in the Kepler and related problems

الأصل · EN

The technique of reduction of order developed by Nucci (J Math Phys 37 (1996) 1772-1775) is used to produce nonlocal symmetries additional to those reported by Krause (J Math Phys 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.