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Celestial Mechanics and Dynamical Astronomy

, Volume 87, Issue 4, pp 353–369 | Cite as

Solution of the Sitnikov Problem

  • S. B. Faruque
Article

Abstract

A new analytic expression for the position of the infinitesimal body in the elliptic Sitnikov problem is presented. This solution is valid for small bounded oscillations in cases of moderate primary eccentricities. We first linearize the problem and obtain solution to this Hill's type equation. After that the lowest order nonlinear force is added to the problem. The final solution to the equation with nonlinear force included is obtained through first the use of a Courant and Snyder transformation followed by the Lindstedt–Poincaré perturbation method and again an application of Courant and Snyder transformation. The solution thus obtained is compared with existing solutions, and satisfactory agreement is found.

Sitnikov problem analytic solution perturbation celestial mechanics restricted three-body problem 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S. B. Faruque
    • 1
  1. 1.Department of PhysicsShah Jalal University of Science and TechnologySylhetBangladesh, e-mail

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