In this lesson, we learn about non-linear autonomous systems and how to sketch their trajectories. Specifically, we focus on a non-linear pendulum and how to find its critical points. Critical points are points where the right-hand side of the equations is zero, and the velocity vector is also zero. By finding these critical points, we can better understand the motion of the system. While non-linear systems can be difficult to solve, physical intuition can help us locate critical points and gain qualitative information about the system's behavior.
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum -- Lecture 31. Some very deep non-linear ODE discussion.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.
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