On the Stability of Equilibrium Positions in the Circular Restricted Four-Body Problem

  • Dzmitry A. Budzko
  • Alexander N. Prokopenya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

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.

Keywords

Equilibrium Point Equilibrium Position Equilibrium Solution Canonical Variable Canonical Transformation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dzmitry A. Budzko
    • 1
  • Alexander N. Prokopenya
    • 2
    • 3
  1. 1.Brest State UniversityBrestBelarus
  2. 2.Collegium Mazovia in SiedlceSiedlcePoland
  3. 3.Brest State Technical UniversityBrestBelarus

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