Abstract:
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, satellite, oscillations, orbital stability, Hamiltonian system, local coordinates, normal form.
This work was supported by the grant of the Russian Science Foundation (project No. 19-11-00116) at
the Moscow Aviation Institute (National Research University).
Citation:
B. S. Bardin, E. A. Chekina, A. M. Chekin, “On the Orbital Stability of Pendulum Oscillations
of a Dynamically Symmetric Satellite”, Rus. J. Nonlin. Dyn., 18:4 (2022), 589–607
\Bibitem{BarCheChe22}
\by B. S. Bardin, E. A. Chekina, A. M. Chekin
\paper On the Orbital Stability of Pendulum Oscillations
of a Dynamically Symmetric Satellite
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 4
\pages 589--607
\mathnet{http://mi.mathnet.ru/nd813}
\crossref{https://doi.org/10.20537/nd221211}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4527640}
Citation in format AMSBIB
Contact us: