Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite

Mathematics

Scientific paper

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Poisson Equation, Rigid Structures, Satellite Rotation, Spin Dynamics, Tumbling Motion, Attitude Stability, Differential Equations, Gravity Gradient Satellites, Mathematical Models, Satellite Attitude Control, Secular Variations

Scientific paper

A mathematical model is developed for studying the effects of gravity gradient torque on the attitude stability of a tumbling triaxial rigid satellite. Poisson equations are used to investigate the rotation of the satellite (which is in elliptical orbit about an attracting point mass) about its center of mass. An averaging method is employed to obtain an intermediate set of differential equations for the nonresonant, secular behavior of the osculating elements which describe the rotational motions of the satellite, and the averaged equations are then integrated to obtain long-term secular solutions for the osculating elements.

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