Abstract
The Kustaanheimo-Stiefel (KS) transformation is shown to follow naturally from the general solution of the two-body motion if ‘half-arguments’ are introduced. Application to collision orbits and to the exact triangular solutions of Lagrange (vide E. Stiefel and G. Scheifele: 1971,Linear and Regular Celestial Mechanics, Springer, Berlin-Heidelberg-New York, p. 23–35).
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Abbreviations
- x :
-
Position vector (x, y, z)
- r=|x|:
-
Distance from the origin
- 1/2h :
-
Energy constant or Kepler motion
- c :
-
Angular momentum vector of Kepler motion
- t :
-
physical time ()·=d/dt ()
- τ:
-
new independent variable ()′=d/dτ ()
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Note by editor: This is the well-known Three-dimensional regularization, published in 1965 by P. Kustaanheimo and E. Stiefel, ‘Perturbation Theory of Kepler Motion Based on Spinor Regularization’,J. reine angewandte Mathematik 218, 204. The present article was written during Professor Volk's stay at the Zurich Technische Hochschule in 1972, when he also celebrated his 80th birthday.
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Volk, O. Concerning the derivation of the KS-transformation. Celestial Mechanics 8, 297–305 (1973). https://doi.org/10.1007/BF01231432
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DOI: https://doi.org/10.1007/BF01231432