Abstract:
We consider the stability of planar periodic Mercury-type rotations of a rigid body around its center of mass in an elliptical orbit in a central Newtonian field of forces. Mercurytype rotations mean that the body makes 3 turns around its center of mass during 2 revolutions of the center of mass in its orbit (resonance 3:2). These rotations can be 1) symmetrical 2π-periodic, 2) symmetrical 4π-periodic and 3) asymmetrical 4π-periodic. The stability of rotations of type 1) was investigated by A.P. Markeev. In our paper we present a nonlinear stability analysis for some rotations of types 2) and 3) in 3rd- and 4th-order resonant cases, in the nonresonant case and at the boundaries of regions of linear stability.
\Bibitem{ChuSte17}
\by Tatyana E. Churkina, Sergey Y. Stepanov
\paper On the Stability of Periodic Mercury-type Rotations
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 7
\pages 851--864
\mathnet{http://mi.mathnet.ru/rcd295}
\crossref{https://doi.org/10.1134/S1560354717070073}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042477532}
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https://www.mathnet.ru/eng/rcd295
https://www.mathnet.ru/eng/rcd/v22/i7/p851
This publication is cited in the following 2 articles:
X. Zhong, J. Zhao, K. Yu, M. Xu, “On the stability of periodic motions of a two-body system with flexible connection in an elliptical orbit”, Nonlinear Dyn., 104:4 (2021), 3479–3496
T Churkina, “On stability of planar periodic motions of a satellite in vicinity of resonant rotation”, IOP Conf. Ser.: Mater. Sci. Eng., 927:1 (2020), 012004
Citation in format AMSBIB
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