Geodesic
Lineaer analysis of stability the planar oscillations of a satellite being a plate in a circular orbit
Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 181-190 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the motion of a satellite (a rigid body) in a circular orbit about its centre of mass. The satellite is subject to the central Newtonian gravitational field. The satellite's principal central moments of inertia $A$, $B$ and $C$ are assumed to satisfy the equation $B=A+C$. This equation holds for thin plates. Particular motions occur when the plate executes pendulum-like oscillations of an arbitrary amplitude in the plane of the orbit. A linear analysis of the orbital stability of this motion is carried out. In the plane of parameters of the problem (an amplitude of oscillations and an inertial parameter) domains of orbital linear stability and instability of oscillations of the satellite are obtained both numerically and analytically.
Mots-clés : satellite, action–angle variables
Keywords: orbital stability, parametric resonance, Deprit–Hori method. 
@article{ND_2005_1_2_a1,
     author = {O. V. Kholostova},
     title = {Lineaer analysis of stability the planar oscillations of a satellite being a plate in a circular orbit},
     journal = {Russian journal of nonlinear dynamics},
     pages = {181--190},
     year = {2005},
     volume = {1},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2005_1_2_a1/}
}
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O. V. Kholostova. Lineaer analysis of stability the planar oscillations of a satellite being a plate in a circular orbit. Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 181-190. http://geodesic.mathdoc.fr/item/ND_2005_1_2_a1/