|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Multiple issues|
| | The author is called Wilber Pegues. Mississippi is where his house is. Invoicing is my profession. Doing ballet is some thing she would never give up.<br><br>Feel free to visit my web blog - clairvoyant psychic ([http://www.khuplaza.com/dent/14869889 khuplaza.com]) |
| {{orphan|date=October 2011}}
| |
| {{expert-subject|date=June 2009}}
| |
| {{unreferenced|date=January 2009}}
| |
| }}
| |
| | |
| The '''Chetayev instability theorem''' for [[dynamical system]]s states that if there exists for the system <math>\dot{\textbf{x}} = X(\textbf{x})</math> a function V('''x''') such that | |
| # in any arbitrarily small neighborhood of the origin there is a region D<sub>1</sub> in which V('''x''') > 0 and on whose boundaries V('''x''') = 0;
| |
| # at all points of the region in which V('''x''') > 0 the [[Total derivative|total time derivative]] <math>\dot{V}(\textbf{x})</math> assumes positive values along every trajectory of <math>\dot{\textbf{x}} = X(\textbf{x})</math>
| |
| # the origin is a [[Boundary (topology)|boundary point]] of D<sub>1</sub>;
| |
| | |
| then the trivial solution is unstable.
| |
| | |
| This theorem is somewhat less restrictive than the [[Lyapunov instability theorem]]s, since a complete sphere (circle) around the origin for which V and <math>\dot{V}</math> both are of the same sign does not have to be produced..
| |
| | |
| == See also ==
| |
| * [[Chetayev Nikolay Gurievich]]
| |
| | |
| [[Category:Theorems in dynamical systems]]
| |
Latest revision as of 20:27, 9 September 2014
The author is called Wilber Pegues. Mississippi is where his house is. Invoicing is my profession. Doing ballet is some thing she would never give up.
Feel free to visit my web blog - clairvoyant psychic (khuplaza.com)