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/ω0, wheren is the orbital mean motion of the center of mass andω0 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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Cochran, J.E. Effects of gravity-gradient torque on the rotational motion of A triaxial satellite in a precessing elliptic orbit. Celestial Mechanics 6, 127–150 (1972). https://doi.org/10.1007/BF01227777
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DOI: https://doi.org/10.1007/BF01227777