Abstract:
We consider the situation where three heavy gravitational bodies form the Lagrange configuration
rotating in a fixed plane and the fourth body of negligible mass moves in this plane. We
present three cases of so-called libration points and we study their stability using linear approximation
and KAM theory. In some situations we prove the Lyapunov stability for generic values
of some parameter of the problem.
Keywords:
Lagrange configuration, libration point, stability.
Citation:
A. Ligeza, H. Zoladek, “Qualitative Analysis of Some Libration Points in the
Restricted Four-body Problem”, Rus. J. Nonlin. Dyn., 17:4 (2021), 369–390
\Bibitem{LigZol21}
\by A. Ligeza, H. Zoladek
\paper Qualitative Analysis of Some Libration Points in the
Restricted Four-body Problem
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 4
\pages 369--390
\mathnet{http://mi.mathnet.ru/nd764}
\crossref{https://doi.org/10.20537/nd210402}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123284614}
Linking options:
https://www.mathnet.ru/eng/nd764
https://www.mathnet.ru/eng/nd/v17/i4/p369
This publication is cited in the following 1 articles:
Henryk Żołądek, “Normal forms, invariant manifolds and Lyapunov theorems”, CAM, 15:2 (2023), 300
Citation in format AMSBIB
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