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On the stability of equilibrium positions in the circular restricted four-body problem. (English) Zbl 1343.70013

Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 13th international workshop, CASC 2011, Kassel, Germany, September 5–9, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-23567-2/pbk). Lecture Notes in Computer Science 6885, 88-100 (2011).
Summary: We consider the stability of equilibrium positions in the planar circular restricted four-body problem formulated on the basis of Lagrange’s triangular solution of the three-body problem. The stability problem is solved in a strict nonlinear formulation on the basis of Arnold-Moser and Markeev theorems. Peculiar properties of the Hamiltonian normalization are discussed, and the influence of the third and fourth order resonances on stability of the equilibrium positions has been analyzed.
For the entire collection see [Zbl 1221.68017].

MSC:

70F10 \(n\)-body problems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
68W30 Symbolic computation and algebraic computation

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