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Studying Stability of the Equilibrium Solutions in the Restricted Many-Body Problems
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| Organization: | Brest State Technical University |
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2003 International Mathematica Symposium
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Imperial College, London
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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.
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equilibrium solutions, many-body problems, radial equilibrium solutions
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