Reserch institute of applaied mathemetics and mechanics of Tomsk state university, Tomsk, Russia
The brief summary of results obtained by authors during the development of efficient algorithms and programms for numerical prediction of the motion of earth's satellites (ESs) and for solving a set practical problems so as investigation of the gravitational field and determinatoin of geodynamical parameters is given. High accuracy of our algorithms has been obtaind by following way. Changing to the Kustaanheimo-Stiefel (KS) variables enable us to regularise and to stabilize equtions of ESs motioin, applying the method of variation of arbitrary constants to equations in KS variables yields eguations in regular elements, the right side of which are slowly varying function of time. Algorithms of the Encke type are used to save computer RAM and increase operating speed. The new so-called variational Encke algorithms in KS variables developed by Sharkovskii in our department are the most efficient. An analysis of the application of various numerical algorithms to problems of prediction of ES motion has shown that Everhart's method is most efficient of them. Using Everhart's method together with the equations of motion in stabilized and regularized form enables one to predict ES motion with subcemtimeterous accuracy. Mathematical model of perturbing forces is calculated with the same accuracy. Simultaneous integration of the equations of motion and the variational equations by mumerical methods with a varial step involvs unprodactiv computer time. For this reason, we have developed, and implemented in the contex of Everhart's method an algorithm for parallel (but not simultaneous) integration of the equations of ES motion and the system of variational equations. Computer implementation of the described alghorithms has enabled us to formulate a series of software packages for practical use.