Geodesic
On the Orbital Stability of Pendulum Oscillations
Russian journal of nonlinear dynamics, Tome 18 (2022) no. 4, pp. 589-607

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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 [1], 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.
Keywords: rigid body, orbital stability, Hamiltonian system, local coordinates, normal form.
Mots-clés : satellite, oscillations 
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     author = {B. S. Bardin and E. A. Chekina and A. M. Chekin},
     title = {On the {Orbital} {Stability} of {Pendulum} {Oscillations}},
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     pages = {589--607},
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     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2022_18_4_a8/}
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B. S. Bardin; E. A. Chekina; A. M. Chekin. On the Orbital Stability of Pendulum Oscillations. Russian journal of nonlinear dynamics, Tome 18 (2022) no. 4, pp. 589-607. http://geodesic.mathdoc.fr/item/ND_2022_18_4_a8/