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| | The author's name is Andera and she thinks it sounds fairly good. My working day job is an information officer but I've already applied for another 1. The favorite pastime for him and his children is style and he'll be starting some thing else along with it. Ohio is where her home is.<br><br>my blog :: are psychics real ([http://www.indosfriends.com/profile-253/info/ http://www.indosfriends.com/]) |
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| {{expert-subject|date=June 2009}}
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| 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;
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| # 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>
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| # the origin is a [[Boundary (topology)|boundary point]] of D<sub>1</sub>;
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| then the trivial solution is unstable.
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| 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..
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| == See also ==
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| * [[Chetayev Nikolay Gurievich]]
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| [[Category:Theorems in dynamical systems]]
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Revision as of 19:09, 20 February 2014
The author's name is Andera and she thinks it sounds fairly good. My working day job is an information officer but I've already applied for another 1. The favorite pastime for him and his children is style and he'll be starting some thing else along with it. Ohio is where her home is.
my blog :: are psychics real (http://www.indosfriends.com/)