| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 97 === The main topic of this article discusses the motion of the ideal pendulum and its perturbation. First, we introduce the partial differential equations and their classification, and we give some practical problems whose mathematical models are systems of linear hyperbolic equations. Next, we study the classical Elliptic functions and one application in solving a nonlinear equation. Moreover, we use the Jacobian Elliptic function to analyze the Sine-Gordon equation to derive the exact solutions, the periods, and to sketch the phase portraits. Finally, we focus on the perturbed pendulum. We do qualitative analysis by using the tools of dynamical system. We find out that even if two initial conditions are close, their behaviors will have big difference in a later time. The phenomenon is called Chaos, a field which still much open.
|
|---|
