Implicit Single-Sequence Methods for Integrating Orbits

Details Implicit Single-Sequence Methods for Integrating Orbits Implicit Single-Sequence Methods for Integrating Orbits

Aug 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10...35e&link_type=abstract

Celestial Mechanics, Volume 10, Issue 1, pp.35-55

Computer Science

68

Scientific paper

The solutions ofddot x = F(x,t), and alsodot x = F(x,t), are developed in truncated series in timet whose coefficients are found empirically. The series ending in thet 6 term yields a position at a final prechosen time that is accurate through 9th order in the sequence size. This is achieved by using Gauss-Radau and Gauss-Lobatto spacings for the several substeps within each sequence. This timeseries method is the same in principle as implicit Runge-Kutta forms, including some not described previously. In some orders these methods are unconditionally stable (A-stable). In the time-series formulation the implicit system converges rapidly. For integrating a test orbit the method is found to be about twice as fast as high-order explicit Runge-Kutta-Nyström-Fehlberg methods at the same accuracies. Both the Cowell and the Encke equations are solved for the test orbit, the latter being 35% faster. It is shown that the Encke equations are particularly well-adapted to treating close encounters when used with a single-sequence integrator (such as this one) provided that the reference orbit is re-initialized at the start of each sequence. This use of Encke equations is compared with the use of regularized Cowell equations.

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