Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On singularities of autonomous implicit ordinary differential equations
 IEEE transactions on circuits and systems. 1, Fundamental theory and applications 50 (2003), No.7, pp.922931 ISSN: 10577122 ISSN: 15498328 

 English 
 Journal Article 
 Fraunhofer HHI () 
Abstract
Implicit ordinary differential equations A(x)(x) over dot = g(x) with A(x) being an n x n matrix depending on x are investigated about their singular points, i.e., inconsistent points in the closure of the set of consistent points. Sufficient conditions are given that ensure that around such points, the above differential equation can be diffeomorphically transformed into the normal form x(1)(r) . (x) over dot(1) = +/1, (x) over dot(2) = 0, ..., (x) over dot(nm) = 0, Xnm+1 = 0,... , x(n) = 0 for some r greater than or equal to 1 and some m, 0 less than or equal to m < n. These results are applied to examples from several fields of application, including an electrical network having impasse points.