Efficient Orbit Integration by Scaling and Rotation for Consistency of Kepler Energy, Laplace Integral, and Angular Momentum Direction

Details Efficient Orbit Integration by Scaling and Rotation for Consistency of Kepler Energy, Laplace Integral, and Angular Momentum Direction Efficient Orbit Integration by Scaling and Rotation for Consistency of Kepler Energy, Laplace Integral, and Angular Momentum Direction

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aj....126.3138f&link_type=abstract

The Astronomical Journal, Volume 126, Issue 6, pp. 3138-3142.

Astronomy and Astrophysics

Astronomy

16

Celestial Mechanics, Methods: N-Body Simulations

Scientific paper

By adding the orbital angular momentum vector as another auxiliary quantity to be integrated, we extend our scaling methods to integrate quasi-Keplerian orbits numerically in order to suppress the growth of integration errors in the inclination and the longitude of the ascending node. This time, the method follows the time evolution of the angular momentum vector, as well as the time development of the Kepler energy and/or the Laplace integral, in addition to integrating the usual equation of motion. By using a rotation that is independent of the application of the spatial scaling, the new method adjusts the position and velocity integrated rigorously at each integration step in order to align both perpendicular to the integrated angular momentum vector. The direction and the angle of the rotation are determined uniquely from the position, the velocity, and the angular momentum vector integrated. As with the original scaling methods, the new method is simple to implement, fast to compute, and applicable to a wide variety of integration methods, perturbation types, and complexities of problems. Although this addition provides no significant decrease in the position error, the new method is superior to the original scaling methods in the sense that it enhances the quality of the integration by significantly reducing the errors of the orbital plane at the cost of a negligibly small amount of additional computation.

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