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Celestial Mechanics and Dynamical Astronomy

, Volume 68, Issue 2, pp 151–162 | Cite as

Regular and Chaotic Solutions of the Sitnikov Problem near the 3/2 Commensurability

  • M. A. Jalali
  • S. H. Pourtakdoust
Article

Abstract

Regular solutions at the 3/2 commensurability are investigated forSitnikov’s problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3πperiodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances.

Sitnikov’s problem periodic motion resonances chaotic behavior 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • M. A. Jalali
    • 1
  • S. H. Pourtakdoust
    • 2
  1. 1.Mechanical Engineering Department, Applied Mechanics DivisionIran
  2. 2.Mechanical Engineering Department, Aerospace DivisionSharif University of TechnologyTehranIran

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