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 Nelin. Dinam., 2017, Volume 13, Number 4, Pages 519–531 (Mi nd582)

On the 75th birthday of A.P.Markeev

Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction

A. A. Burovab, I. I. Kosenkoac

a Dorodnitsyn Computing Center of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Higher School of Economics (National Research University), ul. Myasnitskaya 20, Moscow, 101000, Russia
c Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993, Russia

Abstract: Within the framework of the so-called satellite approximation, configurations of the relative equilibrium are built and their stability is analyzed. In this case the elliptic Keplerian motion of the satellite/the spacecraft tight group mass center is predefined. The attitude motion of the system does not influence its orbital motion. The principal central axes of inertia are assumed to move as a rigid body. Simultaneously masses of the body can redistribute in a way such that the values of moments of inertia can change. Thus, all configurations can perform pulsing motions changing it own dimensions. One obtains a system of equations of motion for such a compound satellite. It turns out that the resulting system of equations is similar to the well-known equation of V.V.Beletsky for the satellite in elliptic orbit planar oscillations. We use true anomaly as an independent variable as it is in the Beletsky equation. It turned out that there are planar pendulum-like librations of the whole system which may be regarded as perturbations of the mathematical pendulum. One can introduce action-angle variables in this case and can construct the dynamics of mappings over the non-autonomous perturbation period. As a result, one is able to apply the well-known Moser theorem on an invariant curve for twisting maps of annulus. After that one can get a general picture of motion in the case of the system planar oscillations. So, the whole description in the paper splits into two topics: (a) general dynamical analysis of the satellite planar attitude motion using KAM theory; (b) construction of periodic solutions families depending on the perturbation parameter and rising from equilibrium as the perturbation value grows. The latter families depend on the parameter of the perturbation and are absent in the non-perturbed problem.

Keywords: KAM theory, Moser theorem on invariant curve, action-angle variables, periodic solutions, analytical developments

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00625a Russian Science Foundation 14-21-00068

DOI: https://doi.org/10.20537/nd1704005

Full text: PDF file (379 kB)
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UDC: 629.195.1+531.1
MSC: 00A71, 37J25, 37J40, 37J45, 68U20, 70E55, 74H15
Accepted:09.11.2017

Citation: A. A. Burov, I. I. Kosenko, “Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction”, Nelin. Dinam., 13:4 (2017), 519–531

Citation in format AMSBIB
\Bibitem{BurKos17} \by A.~A.~Burov, I.~I.~Kosenko \paper Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction \jour Nelin. Dinam. \yr 2017 \vol 13 \issue 4 \pages 519--531 \mathnet{http://mi.mathnet.ru/nd582} \crossref{https://doi.org/10.20537/nd1704005} \elib{http://elibrary.ru/item.asp?id=30780698}