Geometric Methods in Study of the Stability of Some Dynamical Systems
نویسندگان
چکیده
In this paper we aim to analyse the stability of two dynamical systems given by differential equations or by systems of differential equations. The first model is a mechanical system which is described by a system of differential equations of the first degree. We study the stability of this system using the method of the Lyapunov function. The second studied model is the model of a vibrant tool machine described by a differential equation of second degree with two delay arguments. For the study of the stability of these models, we use the stage analysis of the differential equations systems with delayed arguments. 1 The Study of the Stability of a Dynamical System Let us consider the dynamical system presented in Figure 1: This mechanical system is described by the dynamical system of first degree
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