PERIODIC SOLUTIONS ASSOCIATED WITH GRAVITY-GRADIENT-ORIENTED SYSTEM .I. ANALYTICAL AND NUMERICAL DETERMINATION

Analytical and numerical determination. Periodic solutions for an arbitrarily shaped, gravity-gradient stabilized satellite, free to librate in the orbital plane are studied, using analytical and numerical techniques. For motion in a circular orbit, a closed form solution in terms of the elliptic sine function is obtained. For the more general case of motion in an elliptic orbit the method of harmonic balance provides, in principal, the periodic solutions of the problem. Transformation method for determining the complete set of periodic solutions of the problem is also presented.