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Studying Stability of the Equilibrium Solutions in the Restricted Many-Body Problems

Alexander N. Prokopenya
Organization: Brest State Technical University

2003 International Mathematica Symposium
Conference location

Imperial College, London

We study the stability of the equilibrium solutions in the elliptic restricted many-body problems using Mathematica. The calculations done in the case of five interacting bodies have shown that the radial equilibrium solutions are unstable for any value of the mass m0 of the central body, while some bisector equilibrium solutions are stable in linear approximation if m0 is sufficiently large. However, there is a domain of instability of the bisector solutions in the vicinity of the resonant point. Its boundaries are calculated with the method of infinite determinants.

*Science > Physics > Astrophysics

equilibrium solutions, many-body problems, radial equilibrium solutions
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