The Instability of the Rhombus-Like Central Configurations in Newton 9-Body Problem
- 418 Downloads
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.
KeywordsLinear Stability Computer Algebra Computer Algebra System Restricted Problem Elliptic Case
Unable to display preview. Download preview PDF.
- 1.Grebenikov, E.A., Kozak-Skoworodkin, D., Jakubiak, M.: Methods of Computer Algebra in Many-Body Problem (in Russian); Published by UFP, Moscow (2002)Google Scholar
- 3.Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media/ Cambridge University Press (1999)Google Scholar
- 4.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)Google Scholar
- 5.Lyapunov, A.M.: General Problem on Stability of Motion (in Russian). The USSR Academy of Sciences, Moscow (1954)Google Scholar
- 6.Stepanov, V.V.: Course of Differential Equations (in Russian). Nauka, Moscow (1968)Google Scholar
- 7.Arnold, V.I.: About stability of equilibrium positions of Hamiltonian systems in general elliptic case (in Russian). DAN USSR 137, 255–257 (1961)Google Scholar
- 8.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)Google Scholar