Application of computer algebra to the investigation of the orbital satellite motion

A.F. BRAGAZIN, I.P. SHMYGLEVSKY NPO “ENERGIJA” , MOSCOW, USSR 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. Solution for the problems of navigation and center mass motion on the board of satellite put on the suitable claim on the choice of parameters, which describe the perturbed orbital motion. Besides the natural requirement of the effective calculation process and the absence of singularity in the equations of motion it is useful to have the uniform mathematical description for the angular motion and for the motion of the center of mass. In the present paper we use for determining the spatial orientation of the orbit and the satellite position on the orbit the quaternion II (mo, ~1, 9r2, 7r3) for transformations from the inertial geocentrical basis I to the orbital basis Q with origin in the center of mass of satellite and the axes, which are determined from the formula