On the stability of equilibrium positions in the circular restricted four-body problem

Authors:
Dzmitry A. Budzko;Alexander N. Prokopenya
Affiliations:
Brest State University, Brest, Belarus;Collegium Mazovia in Siedlce, Siedlce, Poland and Brest State Technical University, Brest, Belarus
Venue:
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Year:
2011

Citing 2
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Abstract

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.