Studies in the Application of Recurrence Relations to Special Perturbation Methods. V: Reduction in the Number of Auxiliary Variables, and Automatic StepLength Adjustment by Reverse Integration, with Application to the Restricted ThreeBody Problem
Abstract
The procedure of numerical integration of the elliptic three dimensional restricted threebody problem by the use of recurrence relations to evaluate successively higher derivatives of the relative position and velocity vectors of the bodies and of the variational matrix is investigated. A set of recurrence relations is developed which involves the introduction of fewer auxiliary variables than in previous papers of this series, while the recurrence relations themselves are of a simpler form than those in other treatments involving the same number of such auxiliary variables. A technique for automatic adjustment of the integration steplength at each point in the orbit, such that the local truncation error remains close to, but always less than, some specified amount, is incorporated. This technique involves the comparison of preintegration values with those obtained after consecutive forward and reverse integration steps, and has decided advantages over stepadjustment methods currently in use. Both these modifications to previous techniques are shown, by presentation of sample computational results, to represent considerable savings in machine time for a given calculation and desired accuracy; these savings are generally around a factor of two and become greater as the desired accuracy in the computations increases.
 Publication:

Celestial Mechanics
 Pub Date:
 February 1979
 DOI:
 10.1007/BF01796087
 Bibcode:
 1979CeMec..19..147E
 Keywords:

 Numerical Integration;
 Orbit Calculation;
 Perturbation Theory;
 Three Body Problem;
 Algorithms;
 Many Body Problem;
 Run Time (Computers);
 Astronomy