Abstract
We consider the relation between the Lyapunov instability of Lagrange equilateral triangle solutions and their orbital instability. We present a theorem on the orbital instability of Lagrange solutions. This theorem is extended to the planarn-body problem.
References
L. A. Pars,Analytic Dynamics [in Russian], Nauka, Moscow 1971.
S. P. Sosnitskii, “On the rough instability of equilibrium of systems with gyroscopic forces,” in:Problems of Stability in Operationof Navigation Systems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988).
A. M. Lyapunov,General Problem on Stability of Motion [in Russian], ONTI, Moscow-Leningrad 1935.
A. Whitner,Principles of Analytic Mechanics [in Russian], Nauka, Moscow 1967.
Yu. D. Sokolov,Singular Trajectories of a System of Free Mass Points [in Russian], Ukrainian Academy of Sciences, Kiev 1951.
G. N. Duboshin,Celestial Mechanics. Analytic and Qualitative Methods [in Russian], Nauka, Moscow 1964.
E. T. Whittaker,Analytic Dynamics [in Russian], Gosnauchtekhizdat, Moscow-Leningrad 1937.
V. I. Arnold, V. V, Koslov, and A. I. Neishtadt, “Mathematical aspects of classical and celestial mechanics,” in:VINITI Series inContemporary Problems in Mathematics [in Russian], VINITI, Vol. 3, Moscow (1985).
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Sosnitskii, S.P. On the instability of lagrange solutions in the three-body problem. Ukr Math J 48, 1790–1796 (1996). https://doi.org/10.1007/BF02529501
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DOI: https://doi.org/10.1007/BF02529501