Abstract
In the publication Baumgarte and Stiefel (1974a) a stabilization of the Keplerian motion was offered by making use of a manipulation of the Hamiltonian. By this stabilization technique the given HamiltonianH(p i,q i) is replaced by a new HamiltonianH *, which leads to Lyapunov-stable differential equations of motion.
Whereas, in the quoted publication, the physical timet was used as the independent variable we now develop a generalization which allows to combine the stabilization with the introduction of a new independent variables. Such a fictitious times is popular for achieving an analytic step-size adaptation (Baumgarte and Stiefel, 1974c). Perturbations of Kepler motion are discussed.
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References
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Baumgarte, J. and Stiefel, E.: 1974a,Celes. Mech. 10, 71–85.
Baumgarte, J. and Stiefel, E.: 1974b,Mech. Res. Comm. 1, 49–50.
Baumgarte, J. and Stiefel, E.: 1974c, in D. G. Bettis (ed.),Lecture Notes in Mathematics, Springer Verlag, Heidelberg, Vol.362, pp. 207–236.
Beaudet, P. R.: 1974, ‘Dynamic Stabilization and Error Propagation in Perturbed Keplerian Motion’, Prepared by Computer Sciences Corporation for Goddard Space Flight Center, Contract No. NAS 11 999, Task Assignment No. 086.
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Baumgarte, J. Stabilized Kepler motion connected with analytic step adaptation. Celestial Mechanics 13, 105–109 (1976). https://doi.org/10.1007/BF01228537
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DOI: https://doi.org/10.1007/BF01228537