Abstract
E.A.Grebenikov and A.N.Prokopenya proved that rhombus-like central configuration in Newton 5-body problem is unstable. In this article, the problem of existence and stability of the rhombus-like central configurations in Newton 9-body problem, which consists of two homothetic rhombuses, is studied. It is proved that these central configurations are unstable. All computations are executed by means of computer algebra system Mathematica.
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Grebenikov, E.A., Kozak-Skoworodkin, D., Jakubiak, M.: Methods of Computer Algebra in Many-Body Problem (in Russian); Published by UFP, Moscow (2002)
Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton Univ. Press, Princeton (1941)
Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media/ Cambridge University Press (1999)
Abalakin, V.K., Aksenov, E.P., Grebenikov, E.A., Demin, V.G., Ryabov, Y.A.: Handbook on Celestial Mechanics and Astrodynamics (in Russian). Nauka, Moscow (1976)
Lyapunov, A.M.: General Problem on Stability of Motion (in Russian). The USSR Academy of Sciences, Moscow (1954)
Stepanov, V.V.: Course of Differential Equations (in Russian). Nauka, Moscow (1968)
Arnold, V.I.: About stability of equilibrium positions of Hamiltonian systems in general elliptic case (in Russian). DAN USSR 137, 255–257 (1961)
Grebenikov, E.A., Prokopenya, A.N.: About instability of rhombus-like homographical solutions of Mewton five-body problem (in Russian). In: The Problem of Security Theory and Stability Systems. Published by Computing Center of the Russian Acad. Sci., Moscow (2005)
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Diarova, D., Zemtsova, N.I. (2006). The Instability of the Rhombus-Like Central Configurations in Newton 9-Body Problem. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_11
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DOI: https://doi.org/10.1007/11870814_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45182-2
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