Mathematical Model of Satellite Rotation near Spin-Orbit Resonance 3:2

This paper considers the rotational motion of a satellite equipped with flexible viscoelastic rods in an elliptic orbit. The is modeled as symmetric rigid body pair rigidly attached to it along axis symmetry. A planar case studied, i. e., assumed that satellite’s center mass moves Keplerian orbit lying stationary plane and rotation orthogonal this plane. When are not deformed, principal central moments inertia equal each other. linear bending theory for thin inextensible used describe deformations. functionals elastic dissipative forces introduced according model. asymptotic method motions separation derive equations reflecting influence fluctuations, caused by deformations rods. based on assumption period autonomous oscillations point belonging rod much smaller than characteristic time these oscillations’ decay, which, its turn, system’s whole. That why only induced external inertial taken into account when deriving motion. perturbed described third-order system ordinary differential dimensionless variable ratio absolute value angular velocity mean mass, angle between symmetry fixed anomaly. right-hand sides equation depend anomaly implicitly through true new slow order perform averaging near 3:2 resonance,