Effects of gravity-gradient torque on the rotational motion of A triaxial satellite in a precessing elliptic orbit |
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Authors: | John E. Cochran |
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Affiliation: | (1) Dept. of Aerospace Engineering, Auburn University, Auburn, Ala., USA |
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Abstract: | A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/ 0, wheren is the orbital mean motion of the center of mass and 0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made. |
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