Lie groups of motor integrals of generalized Kepler motion

Details Lie groups of motor integrals of generalized Kepler motion Lie groups of motor integrals of generalized Kepler motion

Apr 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..17..207l&link_type=abstract

Celestial Mechanics, vol. 17, Apr. 1978, p. 207-213.

Mathematics

2

Kepler Laws, Lie Groups, Spinor Groups, Lorentz Transformations, Orthogonal Functions, Rings (Mathematics)

Scientific paper

The singularity of the Kepler motion can be eliminated by means of the spinor regularization. The extensive integrals of the Kepler motion form a Lie algebra with respect to the Poisson bracket operation. Mayer-Guerr (1970) has shown that in the case H greater than 0 the corresponding Lie group is the multiplicative group of all real 4 x 4 unimodular matrices SL(4, R). Kustaanheimo (1972) has posed the problem of the identification of the corresponding Lie groups in the elliptic and parabolic cases. This problem is solved and the concept of the Clifford algebra, which is needed in the solution, is explained.

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