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Russia Dolgoprudnyi; Moscow
Year
2018
Volume
28
Issue
3
Pages
373-394
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Section Mechanics
Title On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders
Author(-s) Safonov A.I.ab, Kholostova O.V.bc
Affiliations Research and Production Company “Infosystem-35”a, Moscow Aviation Instituteb, Moscow Institute of Physics and Technologyc
Abstract The motion of a near-autonomous time-periodic two-degree-of-freedom Hamiltonian system in the vicinity of a linearly stable trivial equilibrium is considered. The values of the problem parameters are supposed to be such that the system implements both a double combinational third-order resonance and a fourth-order resonance. The problem of existence and stability of resonant periodic motions of the system is considered. The study is carried out using as an example the problem of the motion of a dynamically symmetric satellite (a rigid body) relative to the center of mass in the central Newtonian gravitational field in an elliptical orbit with small eccentricity. The satellite's periodic motions generated from its stationary rotations in a circular orbit (hyperboloidal and conical precessions) for the resonant values of the parameters are considered as unperturbed ones. The normalization of the Hamiltonian functions of perturbed motion is performed, and the equilibrium positions of approximate (model) systems are determined. The corresponding resonant periodic motions of the satellite in the vicinity of these unperturbed motions are obtained by the Poincare method, and their geometric interpretation is given. The unstable periodic motions and the motions that are stable for the majority (in the sense of Lebesgue measure) of the initial conditions and formally stable are revealed.
Keywords Hamiltonian system, multiple resonance, stability, periodic motion, dynamically symmetrical satellite, hyperboloidal precession, conical precession
UDC 531.36
MSC 70H05, 70H14, 70H15, 70K45
DOI 10.20537/vm180308
Received 15 August 2018
Language Russian
Citation Safonov A.I., Kholostova O.V. On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 3, pp. 373-394.
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