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Published in:
2011 | OriginalPaper | Chapter
On the Stability of Equilibrium Positions in the Circular Restricted Four-Body Problem
Authors : Dzmitry A. Budzko, Alexander N. Prokopenya
Published in: Computer Algebra in Scientific Computing
Publisher: Springer Berlin Heidelberg
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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.