On the Dumb-Bell Equilibria in the Generalized Sitnikov Problem

DOI10.20537/ND221203zbMath1529.70011OpenAlexW4312560960MaRDI QIDQ6054850

P. S. Krasil'nikov, Unnamed Author

Publication date: 28 September 2023

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/nd812

zbMATH Keywords

linear stabilitybifurcation theorysymmetric/asymmetric dumb-bell

Mathematics Subject Classification ID

Three-body problems (70F07) Stability for nonlinear problems in mechanics (70K20)

Cites Work

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• On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions
• Invariant rotational curves in Sitnikov's problem
• On the families of periodic orbits which bifurcate from the circular Sitnikov motions
• Subharmonic oscillations in the near-circular elliptic Sitnikov problem
• On the manifold ``gravitational propeller in the generalized circular Sitnikov problem
• On the investigation of stability of equilibrium in Sitnikov problem in nonlinear formulation
• Attitude stability of a rigid body placed at an equilibrium point in the restricted problem of three bodies
• The structure of the extended phase space of the Sitnikov problem
• The restricted problem of three bodies with rigid dumb-bell satellite
• Periodic orbits of the Sitnikov problem via a Poincaré map

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