Abstract
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-Gürr has shown that in the caseH>0 the corresponding Lie group is the multiplicative group of all real 4×4 unimodular matrices SL(4,R). Kustaanheimo has posed the problem of the identification of the corresponding Lie groups in the elliptic and parabolic cases. We solve this problem here and use the opportunity to introduce the concept of the Clifford algebra which is needed in our solution.
Similar content being viewed by others
References
Atiyah, M. F., Bott, R., and Shapiro, A.: 1964,Topology 3, 3.
Barut, A. O. and Kleinert, H.: 1967,Phys. Rev. 156, 1541.
Kustaanheimo, P. E.: 1972,Celest. Mech. 6, 52.
Mayer-Gürr, J.: 1970, Über Spinordifferentialgleichungen und deren Lösungen unter besonderer Berücksichtigung des Keplerproblems, Inaugural dissertation, Fachbereich, Math., Freie Univ. Berlin.
Porteous, I. R.: 1969,Topological Geometry, London, Van Nostrand.
Riesz, M.: 1958, Clifford Numbers and Spinors, Lecture series No. 38, Maryland, The Institute for Fluid Dynamics and Applied Mathematics.
Stiefel, E. L. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, New York, Springer-Verlag.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lounesto, P. Lie groups of motor integrals of generalized Kepler motion. Celestial Mechanics 17, 207–213 (1978). https://doi.org/10.1007/BF01232827
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01232827