Efficient Integration of Highly Eccentric Orbits by Quadruple Scaling for Kustaanheimo-Stiefel Regularization

Details Efficient Integration of Highly Eccentric Orbits by Quadruple Scaling for Kustaanheimo-Stiefel Regularization Efficient Integration of Highly Eccentric Orbits by Quadruple Scaling for Kustaanheimo-Stiefel Regularization

Dec 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aj....128.3108f&link_type=abstract

The Astronomical Journal, Volume 128, Issue 6, pp. 3108-3113.

Astronomy and Astrophysics

Astronomy

4

Celestial Mechanics, Methods: Numerical

Scientific paper

We have extended the single scaling method for Kustaanheimo-Stiefel (K-S) regularization by applying different scaling factors to each component of the four-dimensional harmonic oscillator associated with the regularization. This is achieved by monitoring the time development of the total energy of each component of the harmonic oscillator and rescaling the magnitude of the position and velocity of the corresponding component so as to satisfy the defining relation for the harmonic energy. To perform the monitoring increases the number of variables to be integrated per celestial body from 10 to 13; however, the extra cost of computation is still negligible compared with that of the perturbing acceleration. The resulting method of quadruple scaling significantly enhances the numerical stability of orbit integrations. In the case of unperturbed orbits, the new method when applied at every integration step reduces to the machine-epsilon level the errors in all the orbital elements except the mean longitude at epoch, if sufficiently high order integrators are used with sufficiently small step sizes. This remarkable feature is lost when the scaling is applied at every apocenter. In the case of perturbed orbits, we confirm the superiority of the quadruple scaling method applied at every integration step over the other scaling methods for K-S regularized orbital motions unless round-off plays the key role in the accumulation of integration error.

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