Stabilization due to gyroscopic coupling in dual-spin satellites subject to gravitational torques

Solutions homoclinic to regular precessions of a symmetric satellite

“…For overview, we refer to the book of Beletskii (1975) and the paper of Sokolsky (1980). Many aspects of the dynamics of this, and slightly modified systems, were investigated in (Markeev, 1967b;Kane and Marsh, 1971;Longman et al, 1981;Markeev, 1985;Markeev and Shcherbina, 1987;Markeev, 1988;Aboelnaga, 1989) and in many other papers.…”

The Dynamics of a Satellite-Gyrostat with a Single Nonzero Component of the Vector of Gyrostatic Moment

“…For example, the most complete investigation of all equilibrium positions of a gyrostat and of their stability is carried out in [5] and [6] for the case h 1 = 0, h 2 ≠ 0, and h 3 = 0. One also should note papers [7] and [8], where a similar problem was solved only with reference to solution with α = 0, β = 0, and γ = 0.…”

“…Instead of system (5) it is more convenient to use the following system equivalent to it (6) Taking (1) into account, system (6) may be considered as a system of three equations with unknowns α 0 , β 0 , and γ 0 . Another method of closure of equations (6) consists in addition of the condition of orthogonality of the direction cosines,…”

Attitude stability of an orbiting gyrostat in conical equilibrium

“…The condition (6) reduces to (10) after elimination of the cylindrical degeneracy. Stability for this case of equilibrium has been studied by Longman et al 4 Interest centers here on a different subcase, one characterized by a yaw-axis wheel (Fig. 4).…”