The technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772-1775 (1996)] is used to produce nonlocal symmetries in addition to those reported by Krause [J. Math. Phys. 35, 5734-5748 (1994)] 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 generalizations. 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.
NUCCI, M.C., Leach P. G. L. (2001). The harmony in the Kepler and related problems. JOURNAL OF MATHEMATICAL PHYSICS, 42(2), 746-764 [10.1063/1.1337614].
The harmony in the Kepler and related problems
NUCCI, Maria Clara;
2001
Abstract
The technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772-1775 (1996)] is used to produce nonlocal symmetries in addition to those reported by Krause [J. Math. Phys. 35, 5734-5748 (1994)] 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 generalizations. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
