Abstract
В статье приводятся основные этапы алгоритма построения областей устойчивости динамических систем, описываемых линейной гамильтоновой системой вида . Алгоритм основан на методах теории нелинейных колебаний исследования устойчивости стационарных решений линейных дифференциальных уравнений с периодическими коэффициентами, зависящих от малого параметра. Алгоритм реализован с помощью математического пакета Matlab. В качестве приложения рассмотрена задача построения области устойчивости треугольных точек либрации плоской ограниченной эллиптической задачи трех тел 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.
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