Motion of an Infinitesimal Mass in the Field of a Cyclic Kite Configuration of the Second Kind

Abstract

This paper investigates the equations of motion of each of the four-point masses that form a kite configuration of the second kind, relative to the remaining three, which are established in a synodic frame in terms of position vectors, mass parameter and mean motion. By eliminating the position vectors from the equations of four masses, a functional relation between the mean motion and mass parameter has been established, in which the mean motion of the synodic frame can be expressed as a function of the mass parameter. Using this relation, the governing equations for the motion of an infinitesimal mass influenced by the gravitational field of the kite configuration are formulated for all admissible values of the mass parameter and mean motion within their respective domains. These equations are further applied to the Sitnikov problem, where the resulting dynamics are analyzed. Finally, a periodic series solution is constructed through the iteration process of Green’s function.