On the Orbital Stability of Pendulum Oscillations of a Dynamically Symmetric Satellite
Received 10 November 2022; accepted 04 December 2022; published 17 December 2022
2022, Vol. 18, no. 4, pp. 589-607
Author(s): Bardin B. S., Chekina E. A., Chekin A. M.
The orbital stability of planar pendulum-like oscillations of a satellite about its center of mass is investigated. The satellite is supposed to be a dynamically symmetrical rigid body whose center of mass moves in a circular orbit. Using the recently developed approach , local variables are introduced and equations of perturbed motion are obtained in a Hamiltonian form. On the basis of the method of normal forms and KAM theory, a nonlinear analysis is performed and rigorous conclusions on orbital stability are obtained for almost all parameter values. In particular, the so-called case of degeneracy, when it is necessary to take into account terms of order six in the expansion of the Hamiltonian function, is studied.
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