Dynamic Analysis Of Several Non-smooth Spring Oscillator Models

In this thesis,the theory of Filippov system in general plane and the theory of Filippov system with differential inclusion are comprehensively used to study the spring oscillator model of objects moving on horizontal plane and slope under friction.Firstly,the dynamic behavior of objects moving on non-smooth surface is studied according to Newton's law,and then a suitable mathematical model is established.Then,the existence and stability of the equilibrium of the subsystem and the corresponding equilibrium set of the system are studied.Finally,the sliding mode dynamic properties on the switching line and the global dynamic behavior of the system are studied.The first chapter introduces the research background,purpose,significance,present situation and structural arrangement of the article.The second chapter describes the main basic theoretical knowledge.In chapter 3,the dynamic behaviors of two kinds of spring oscillator models with plane motion are studied,one of which is a spring oscillator model with spring fixed end located in the moving direction,and the other is a spring oscillator model with spring fixed end not located in the moving direction.The dynamic behaviors of the two models are described by Newton's first law and Newton's second law.The research of these two models is based on mathematical modeling first.Secondly,the Filippov convex method is used to analyze the sliding mode dynamics properties on the switching line,including the existence of sliding mode domain and the existence of pseudo-equilibrium.Then,by constructing Poincare maps,the global dynamic behavior of the system is analyzed,and it is concluded that the set of points in the sliding mode domain is the pseudo-equilibrium of the system,which is the global attractor of the system and any solution of the system is globally convergent in finite time.Finally,the reliability of the results is verified by numerical simulation.In chapter 4,it is different from the previous chapter in that this chapter considers the global dynamic behavior of the spring oscillator model moving on the slope surface when the moving surface has an inclined angle.Firstly,according to the motion of the object,the mathematical model is established,and the equilibrium is expressed by the monotonicity of the function in the system by turning the system into a plane differential equation.Then,Poincare maps and Filippov convex method are used.The motion trajectory of the system is analyzed,and the conclusion that the set of points in the sliding mode domain is the global attractor of the system and the attractor converges globally in finite time is obtained.Finally,the correctness of the theory is verified by numerical simulation.At the end of the paper,the research work is summarized and the future research direction is prospected.