Plane Motions of a Near Symmetric Satellite about its Mass Center with Rational Rotation Numbers. I. Normal Form in the Regular Case

The equation of plane oscillations of a satellite is a Hamiltonian system with 3/2 d.o.f. Solutions of the form (linear function of time with rational coefficient plus a periodic function) are called Lissajous-type solutions. In case of a near linear system, their stability is studied by use of the normal form method. This leads in a natural way to arbitrary degenerate normal forms. Exponents of first terms that do not vanish are determined by methods of geometry in the power exponent space. Similarly asymptotics of those terms w.r.t. parameter e (the eccentricity) as e \to 0 are studied.