Two examples of how to approximate a nonlinear system with a linear model using linearization. The first example is that of an inverted pendulum which can be used to model physical systems like the Segway, the hover board, landing a first stage of a rocket vertically, or a walking biped robot; the Taylor series is used to generate a linear approximation of the pendulum's motion around an angle for zero. The second example uses the logistic population growth model; the equilibrium points are computed and used to get a linear approximation at each point.
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** Segway photo is licensed under Creative Commons and is courtesy of
Joan Campderrós-i-Canas in Flickr: www.flickr.com/photos/joanet/...
Licence creativecommons.org/licenses/...
** First Stange Falcon 9 landing photo is in the public domain courtesy of SpaceX. The photo can be found on SpaceX Flickr account: www.flickr.com/photos/1306086...
** World population growth image is courtesy of Lauren Manning on Flickr: www.flickr.com/photos/laurenm.... The photo is licensed under Creative Commons: creativecommons.org/licenses/...