Astrophysics and Space Science

, Volume 61, Issue 2, pp 389–409 | Cite as

Three-dimensional periodic oscillations generating from plane periodic ones around the collinear Lagrangian points

  • C. G. Zagouras
  • P. G. Kazantzis


The three families of three-dimensional periodic oscillations which include the infinitesimal periodic oscillations about the Lagrangian equilibrium pointsL1,L2 andL3 are computed for the value μ=0.00095 (Sun-Jupiter case) of the mass parameter. From the first two vertically critical (|a v |=1) members of the familiesa, b andc, six families of periodic orbits in three dimensions are found to bifurcate. These families are presented here together with their stability characteristics. The orbits of the nine families computed are of all types of symmetryA, B andC. Finally, examples of bifurcations between families of three-dimensional periodic solutions of different type of symmetry are given.


Periodic Solution Periodic Orbit Periodic Oscillation Mass Parameter Stability Characteristic 
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Copyright information

© D. Reidel Publishing Company 1979

Authors and Affiliations

  • C. G. Zagouras
    • 1
  • P. G. Kazantzis
    • 2
  1. 1.Dept. of MechanicsUniversity of PatrasGreece
  2. 2.University of GlasgowUK

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