On Nonlinear Resonant Oscillations of a Rigid Body Generated by Its Conical Precessionстатья
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Дата последнего поиска статьи во внешних источниках: 25 апреля 2019 г.
Аннотация:The motion of a dynamically symmetric rigid body relative to its center of mass in the central Newtonian gravitational field in a circular orbit is investigated. In this problem, there is a motion (called conical precession) when the dynamic symmetry axis of the body is always located in the plane perpendicular to the body mass center velocity vector, and is a constant angle with the direction of the mass center radius-vector relative to the attracting center. The article deals with a special case when this angle is 45 degrees, and the ratio of the polar and equatorial principal central moments of inertia of the body is equal to 2/3 or close to it. In this case, the conical precession is stable with respect to the angles that define the position of the symmetry axis in the orbital coordinate system, and to the derivatives in time of these angles. Herewith, the frequencies of small (linear) oscillations of the symmetry axis are equal to or close to one another (that is, the resonance 1:1 is realized). The problem of existence, bifurcations and stability of the body symmetry axis periodic motions generated from its relative (in the orbital coordinate system) equilibrium corresponding to the conical precession is solved by the classical perturbation theory and modern numerical and analytical methods of nonlinear dynamics. The problem of the existence of conditionally periodic motions is also considered.