STUDIES IN THE APPLICATION OF RECURRENCE RELATIONS TO SPECIAL PERTURBATION METHODS .5. REDUCTION IN THE NUMBER OF AUXILIARY VARIABLES, AND AUTOMATIC STEP-LENGTH ADJUSTMENT BY REVERSE INTEGRATION, WITH APPLICATION TO THE RESTRICTED 3-BODY PROBLEM

被引:7
作者
EMSLIE, AG
WALKER, IW
机构
[1] Department of Astronomy, The University, Glasgow
来源
CELESTIAL MECHANICS | 1979年 / 19卷 / 02期
关键词
D O I
10.1007/BF01796087
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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 step-length 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 pre-integration values with those obtained after consecutive forward and reverse integration steps, and has decided advantages over step-adjustment 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. © 1979 D. Reidel Publishing Co.
引用
收藏
页码:147 / 162
页数:16
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