2.1   LINEARISATION

In this section you will learn to

understand the technique of linearisation

linearise a nonlinear system using a change of variable

linearise a nonlinear system using Taylor’s series.
 

The technique of linearisation involves approximating a complicated system of equations with a simpler linear system. We hope to gain insight into the behaviour of the nonlinear system through an analysis of the behaviour of its linearisation. We hope that the nonlinear system will behave locally like its linearisation, at least in a qualitative sense.

2.1.1  Linearisation by change of variable
This method is explained in the course handbook.

2.1.2  Linearisation by Taylor Series
Consider the nonlinear system

The linearisation can be written in the form
 

where J=

is called the Jacobian matrix

The method will be illustrated in the following worked example.

click here for a worked example.