On orbital stability of resonant periodic motions originating from hyperboloidal precession of a dynamically symmetric satellite

Abstract

Abstract Periodic motions arising from Hyperboloidal precession of a dynamically symmetric rigid-body satellite on a circular orbit are studied in this work. There exist two types of these motions categorized by frequencies ^ and co2 of the linearized system: short-periodic motions with period close to 2n/co2 and long-periodic ones with period close to 2?!/^ (co2 > co). These motions describe oscillations of the satellite’s principal axis in the neighbourhood Hyperboloidal precession and can be obtained as small-parameter power series of the oscillation amplitude. It has been shown before that in a resonant case there exist more than one family of long-periodic motions. In this work, families of long-periodic motions originating from Hyperboloidal precession in case of fourth order resonance are computed and analysed.