Graduate Thesis Or Dissertation
 

A study of attitude stability of a symmetrical satellite in a circular orbit

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  • A model for analytical study of the attitude stability of an orbiting satellite consists of a rigid body whose mass center is constrained to move at constant speed in a circular path about the center of an inverse-square force field. The body is assumed to have one axis of inertial symmetry. It is of primary interest here to determine whether the attitude of this symmetric axis is stable in its various equilibrium positions. The stability depends upon two parameters: the ratio of spin velocity about the symmetry axis to orbital angular velocity, and the ratio of the two moments of inertia of the satellite. The equations of motion which govern the deviations of the symmetry axis from its equilibrium configuration are nonlinear in nature. When linearized, the equations show instability in some regions, but everywhere else, the linear approximation is a "critical case" in which the roots of the characteristic equation all have zero real part. When complete nonlinear equations are investigated by means of the direct method of Lyapunov, some region can be specified as Lyapunov stable by using the Hamiltonian function as a Lyapunov function, while there remains a sizeable region where the stability has not been determined, as shown in papers by Pringle and Likins, When equations which are approximated by third and fifth powers are investigated by a series of transformations following Malkin's approach, it is found that if there is instability in the remainder of plane where no conclusion is yet available, it is very weak.
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