Symbolic and Numerical Analysis of the Restricted Five Body Problem Using Computer Algebra

摘要

This paper is devoted to the application of the computer algebra system Mathematica for the investigation of a nonlinear system of algebraic equations with parameters that describes the dynamics of a passively gravitating mass in the space of four bodies forming a central convex deltoid configuration. Domains of existence of solutions in the plane of parameters are found, and the number of solutions depending on the parameters of the system is determined. Bifurcational analysis is performed, and bifurcation curves in the plane of parameters are constructed that separate the domains of parameters with different number of solutions. Corresponding analysis algorithms for the system under examination are developed and implemented in Mathematica.