The circular case of Sitnikov problem is studied here when the infinitesimal body varies its mass according to Jeans law and it is moving along the z-axis which is perpendicular to the orbital plane of the two equal spherical primaries. The two primaries are moving in xy-plane on the same circular path. These two primaries are imposing the Newtonian forces on the third variable mass body but not influenced by it. Stability of equilibrium points is examined followed by the derived equations of motion. The time-series solutions of the equation of motion are performed by using the Lindstedt-Poincaré method which is used to remove the secular term. We have numerically performed the time-series which shows that variation parameters have great impact on it.
Ansari, Abdullah A.; Prasad, Sada N.; and Singh, Chaman
Vertical Motion of the Variable Infinitesimal Mass In the Circular Sitnikov Problem,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 41.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/41