{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

normal_form

# normal_form - Normal Forms Theory CDS140B Lecturer Wang...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Normal Forms Theory CDS140B Lecturer: Wang Sang Koon Winter, 2004 1 Normal Form Theory Introduction. To find a coordinate system where the dynamical system take the “simplest” form. • The method is local in the sense that the coordinate transforms are generated near a know solution, such as a fixed point. • The coordinate transformation will be nonlinear, but these transformation are found by solv- ing a sequence of linear problem. • The structure of the normal form is determined entirely by the nature of the linear part of the problem. Preliminary Preparation. Consider ˙ w = G ( w ) where w ∈ R n , G is C r , and the system has a fixed point at w = w . Then it can be written as (*) ˙ x = Jx + F ( x ) = Jx + F 2 ( x ) + F 3 ( x ) + · · · + F r- 1 ( x ) + O ( | x | r ) where F i ( x ) represent the order i terms in the Taylor expansion of F ( x ). 1 1.1 Simplification of the Second Order Terms Introduce the coordinate transformation x = y + h 2 ( y ) where h 2 ( y ) is second order in...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

normal_form - Normal Forms Theory CDS140B Lecturer Wang...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online