The inclination changes in the problem of two triaxial rigid spheroids

Physics

Scientific paper

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Equations Of Motion, Perturbation Theory, Pitch (Inclination), Rigid Structures, Spheroids, Two Body Problem, Angular Momentum, Hamiltonian Functions, Rotating Bodies, Translational Motion

Scientific paper

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter tau such that t is the hyperelliptic function of tau. The projections H1 and H2 of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of tau. The trajectory in the H1, H2 plane is a part of an ellipse or hyperbola, respectively. If this conical section intersects a certain critical contour, the system is 'bounced' back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.

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