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 circular orbit. The case of hyperboloidal precession is considered. Analytical expressions for normal forms and generating functions depending on frequencies of the system as on parameters are derived. Possible resonances are considered in particular. The 6th order of normalization is achieved. Though the intermediate analytical expressions occupy megabytes of computer's main memory, final ones are quite compact. Obtained analytical expressions are applied to the analysis of stability of small-amplitude periodic motions in the neighbourhood of hyperboloidal precession.