Design of a Spherical Chaotic Oscillator and its Application in Four Cases of Celestial Mechanics

Abstract

This paper presents the procedure for the design of a spherical chaotic system based on the movement of two bodies that interact with each other because of the gravitational force exerted by the body of greater mass concerning the body of smaller mass. Establishing that the secondary body presents a chaotic behavior along its orbit, four cases are determined in which this could happen, which leads to creating a project that simulates each case. During the process, the precision of the results is considered to define the most optimal parameters of the project. The three output signals represent the movement of the secondary body and can be verified by the results obtained from the same system by using Matlab programs that simulate the four cases, respectively. Finally, the complete design of the four cases was performed on an FPGA board, using VHDL code.