Invariance group of the Kepler oscillator problem

Details Invariance group of the Kepler oscillator problem Invariance group of the Kepler oscillator problem

Apr 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979zamm...59..177b&link_type=abstract

Zeitschrift für angewandte Mathematik und Mechanik, vol. 59, Apr. 1979, p. 177-187. In German. Research supported by the Deutsch

Mathematics

1

Celestial Mechanics, Invariance, Kepler Laws, Oscillators, Canonical Forms, Equations Of Motion, Lie Groups, Matrices (Mathematics), Transformations (Mathematics)

Scientific paper

A 6-parametric group of canonical transformations is constructed which leaves invariant the Keplerian motion with the eccentric anomaly as independent variable. This group is isomorphic to the four-dimensional rotational group SO(4). It is characterized by the fact that the momenta are transformed again into momenta. The scheme leading to the construction of the invariance-group SO(4) leads also to the noninvariant algebra so(4, 2) which is important for dynamics of the Keplerian motion, together with the invariant algebra so(4) as subalgebra. In case of plane Keplerian motion the transformations of the momenta are given by the stereographic projection of the rotations of a sphere. By the concretization of abstract isomorphism the KS-transformation is obtained which maps the three-dimensional Keplerian motion into the four-dimensional oscillator motion.

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