Method of averaging
From Wikipedia, the free encyclopedia
In the study of dynamical systems, the method of averaging is used to study certain time-varying systems by analyzing easier, time-invariant systems obtained by averaging the original system.
[edit] Definition
Consider a general, nonlinear dynamical system
where f(t,x) is periodic in t with period T. The corresponding averaged system is
The primary benefit of averaging is that it is usually easier to analyze equilibria (and their stability) of time-invariant (autonomous) systems.
[edit] Example
Consider a simple pendulum whose point of suspension is vibrated vertically by a small amplitude, high frequency signal (this is usually known as dithering). The equation of motion for such a pendulum is given by
where asinωt describes the motion of the suspension point and θ is the angle made by the pendulum with the vertical.
The state space form of this equation is given as
 |
This mathematics-related article is a stub. You can help Wikipedia by expanding it. |
