Abstract
In this paper, the equations of motion for spatial restricted circular three body problem will be established using the cylindrical coordinates. Initial value procedure that can be used to compute both the cylindrical and Cartesian coordinates and velocities is also developed.
Highlights
Depending on the application, a certain coordinate system may be simpler to use than the Cartesian coordinate system
A physical problem with spherical symmetry defined in R3, is usually easier to solve in spherical polar coordinates than in Cartesian coordinates
The change of the dependent and/or independent variables for the differential equations of motion becomes of the focal point of researches in space dynamics
Summary
A certain coordinate system may be simpler to use than the Cartesian coordinate system. The change of the dependent and/or independent variables for the differential equations of motion becomes of the focal point of researches in space dynamics. Some authors proposed successful methods to change of the dependent and/or independent variables so as to regularize the differential equations of motion. Many studies on the applications of these devices for some orbital systems were done for the perturbed two body problem The present paper represents the first phase of our studies towards establishing new differential equations for the different forms of the three body problem using some important coordinate systems. The objective of the present paper, is to establish the equations of motion for spatial restricted circular three body problem in cylindrical coordinates system together with initial value procedure that can be used to compute both the cylindrical and Cartesian coordinates and velocities
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