Solution of the Sitnikov Problem

Details Solution of the Sitnikov Problem Solution of the Sitnikov Problem

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003cemda..87..353f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 87, Issue 4, p. 353-369 (2003).

Astronomy and Astrophysics

Astronomy

9

Scientific paper

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.

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