The algorithms for constructing the boundaries of the stability regions of linear hamiltonian systems by using MATLAB

Abstract

The article presents the main stages of the algorithm for constructing the stability regions of dynamical systems described by a linear Hamiltonian system of the form . The algorithm is based on the methods of the theory of nonlinear oscillations of stability studies of stationary solutions of linear differential equations with periodic coefficients depending on a small parameter. The algorithm is implemented by using Matlab CAS. As an application, we have solved the problem of constructing the stability region of libration points of a flat elliptic restricted three-body problem is analyzed in detail.

Keywords

• Hamiltonian systems
• stability
• the stability region
• periodic solutions
• parameter
• the three-body problem