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This article is cited in 1 scientific paper (total in 1 paper)
Nonlinear physics and mechanics
On the Dumb-Bell Equilibria in the Generalized
Sitnikov Problem
P. S. Krasilnikov, A. R. Ismagilov Moscow Aviation Institute (National research university),
Volokolamskoe sh. 4, Moscow, 125993 Russia
Abstract:
This paper discusses and analyzes the dumb–bell equilibria in a generalized Sitnikov problem.
This has been done by assuming that the dumb–bell is oriented along the normal to the plane
of motion of two primaries. Assuming the orbits of primaries to be circles, we apply bifurcation
theory to investigate the set of equilibria for both symmetrical and asymmetrical dumb–bells.
We also investigate the linear stability of the trivial equilibrium of a symmetrical dumb–bell
in the elliptic Sitnikov problem. In the case of the dumb–bell length $l \geqslant 0.983819$, an instability
of the trivial equilibria for eccentricity $e \in (0, 1)$ is proved.
Keywords:
Sitnikov problem, dumb–bell, equilibrium, linear stability.
Received: 24.10.2022 Accepted: 21.11.2022
Citation:
P. S. Krasilnikov, A. R. Ismagilov, “On the Dumb-Bell Equilibria in the Generalized
Sitnikov Problem”, Rus. J. Nonlin. Dyn., 18:4 (2022), 577–588
Linking options:
https://www.mathnet.ru/eng/nd812 https://www.mathnet.ru/eng/nd/v18/i4/p577
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