The nonlinear pendulum and phugoid oscillation

Description
"Introduction to general nonlinear autonomous systems is given and explained with the help of examples. An autonomous system is the same thing as a vector field, this is analysed and proved with logical statements.The trajectories of this vector field are circles. near an equilibrium an autonomous system is well approximated by a linear system, which we can then analyze using eigenvectors and eigenvalues. Linearization of the autonomous system is described. The nonlinear pendulum and phugoid oscillation are discussed. The bob of a pendulum is attached to a rod, so it can swing clear around the pivot. This system is determined by three parameters, L= length of pendulum, m= mass of bob and g= acceleration of gravity Here it is assumed that the motion is restricted to a plane.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 30: Non-linear Autonomous Systems: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed December 8, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc