Time Regularization of an AdamsMoultonCowell Algorithm
Abstract
This paper deals with the AdamsMoultonCowell multistep integrator, as described by Oestwinter and Cohen (1972). In order to evaluate the accuracy of the method, we started to test it in the case of the unperturbed twobody motion; numerical instability may arise by integrating first order systems. The accuracy is improved by applying a Sundmann transformation of the independent variable. The algorithm is then modified such that the equations of pure keplerian motion are integrated with respect to the new independent variable without truncation error; numerical experiments show the considerable improvement of accuracy and the reduction of computing time for Keplerian motion. If terms of the disturbing function of the Earth are added to the central potential, the timetransformation is less effective. With a modification of this timetransformation as given by Moynot in 1971, it is possible to reduce the propagation of the truncation error in the J2 problem.
 Publication:

Celestial Mechanics
 Pub Date:
 November 1977
 DOI:
 10.1007/BF01232656
 Bibcode:
 1977CeMec..16..291B
 Keywords:

 Algorithms;
 Numerical Integration;
 Orbit Calculation;
 Satellite Orbits;
 Two Body Problem;
 Artificial Satellites;
 Eccentricity;
 Geopotential;
 Independent Variables;
 Kepler Laws;
 Transformations (Mathematics);
 Truncation Errors;
 Astronomy