Symbolic evaluation in the nonlinear mechanical systems

The paper presents the features of a program package “Polymech-symbol” helping to solve some laborious mechanical problems. The package was written by means of the REDUCE system and contains several algorithms in a form of REDUCE procedures. The computer algebra methods may be successfully used for a solving the problems of navigation and defining the trajectory of satellite mass centre motion. The preliminary analytical research provides the effective algorithm for on-board solving the problem of prediction. To assure necessary accuracy, we need to construct several higher approximations. Such sophisticated problem can be solved only with the help of symbolic computations that deal with the processing of cumbersome analytical expressions. For effective analytical investigation such kind of problems the choice of parameters which describe the perturbed orbital motion is critical. In addition to the natural requirements of the calculation process efficiency and the absence of singularities in equations of motion, it is useful to have a unified mathematical description for the angular motion and for the motion of the mass centre. In this paper, for determining the spatial orientation of the orbit and the satellite position on the orbit, we used the quaternion II (TO, ml, 7r2, m) that transforms from the inertial geocentric basis 17 to the orbital basis Q with the origin at the satellite mass centre. The components of II are normalized (ir~ + my + z; + n; = 1). The parameters V., VI, VZ in formulae