1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linearization of non linear systems

  1. Oct 8, 2014 #1
    1. The problem statement, all variables and given/known data
    In my dynamics modelling class, the professor went over an example where we linearize non linear state equations to approximate the behavior. In this case, we are not given an operating point. However, the professor said you can solve for the operating point by setting x' = 0. See the picture below for the notes.

    I don't really understand why we can do this, if we set x' = 0, doesn't this just solve for the max and min values of x. For example if x = displacement, then we get the max and min displacements at a certain point. I tried to do some research but I am still confused.

    2. Relevant equations
    x' = f(x,u)

    3. The attempt at a solution
  2. jcsd
  3. Oct 8, 2014 #2


    User Avatar
    Homework Helper

    A dynamic system can have equilibrium points, where the velocities (##\dot x_i##-s ) are zero, and investigate the motion of the system around these points: If moving out the system slightly from equilibrium, it returns back or goes away, and there are some other possibilities.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted