Numerical stabilization of Keplerian motion

Details Numerical stabilization of Keplerian motion Numerical stabilization of Keplerian motion

Apr 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..26..407z&link_type=abstract

Celestial Mechanics, vol. 26, Apr. 1982, p. 407-412.

Mathematics

Celestial Mechanics, Kepler Laws, Motion Stability, Numerical Stability, Orbital Mechanics, Equations Of Motion, Fourier Series, Numerical Integration, Time Functions, Transformations (Mathematics)

Scientific paper

The time transformation dt/ds = r to the alpha is introduced, and the mean motion for various values of alpha is found. It is shown that the stabilization may be attained by fixing the energy only when alpha = 0 or 1. It is noted that the stabilizing device is different for other values of alpha. Following Baumgarte (1972), the additional control terms are introduced for alpha = 1, 2, and 3/2, and their effect is shown. Attention is also given to the concept of the time element.

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