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Topology of the Negative Energy-Manifold of the Kepler Motion

Published online by Cambridge University Press:  14 August 2015

Junzo Yoshida
Junzo Yoshida*
Affiliation:
Department of Physics, Kyoto Sangyo University, Kita-ku, Kyoto 603, Japan

Extract

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The motion of a particle of mass m according to the central force of Newton, is denoted by where K is a constant. x=0 corresponds to singular points of this equations. The domain of (1), denoted by = (R3 −{0})×R3, is called the phase space of the Kepler motion. In the sequel we set m=K=1 for simplicity and also transform the independent variable from t to s by dt =|x|ds (x≠0), then the Kepler motion in the phase space is written as Further, we shall confine the following discussion to the case of the negative energy value, except the preliminary discussion.

Type
Part I: Stability, N- and 3-Body Problems, Variable Mass
Information
Symposium - International Astronomical Union , Volume 81: Dynamics of the Solar System , 1979 , pp. 45 - 48
Copyright
Copyright © Reidel 1979 

References

1. Moser, J.: Regularization of Kepler's Problem and the Averaging Method on a Manifold. Comm. Pure Apple. Math. 23 (1970), 609–636.Google Scholar
2. Kustaanheimo, P. and Stiefel, E.: Perturbation Theory of Kepler Motion Based on Spinor Regularization. J. Reine Angew. Math. 218 (1965), 204–219.Google Scholar
3. Stiefel, E.L. and Scheifele, G.: Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin 1971, Chap. II, III, and XI.Google Scholar