HYPERBOLOIDAL PRECESSION OF A DYNAMICALLY SYMMETRICAL SATELLITE - CONSTRUCTION OF NORMAL FORMS OF THE HAMILTONIAN

The 'Norma' specialized program package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used in studies of small-amplitude periodic motions in the neighbourhood of regular precessions of a dynamically symmetric satellite on a circula r orbit. The case of hyperboloidal precession is considered. Analytica l expressions for normal forms and generating functions depending on f requencies of the system as on parameters are derived. Possible resona nces are considered in particular. The 6th order of normalization is a chieved. Though the intermediate analytical expressions occupy megabyt es of computer's main memory, final ones are quite compact. Obtained a nalytical expressions are applied to the analysis of stability of smal l-amplitude periodic motions in the neighbourhood of hyperboloidal pre cession.