Gunther Reißig and Holger Boche.
Straightening out trajectories near singular points of implicit differential equations.
Proc. 9th Int. Symp. System-Modelling-Control (SMC), P. S. Szczepaniak, ed.,
Zakopane, Pl., April 27 - May 1, 1998.
Full text.
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Abstract:
Under appropriate assumptions, it is shown that
there is a diffeomorphism
that transforms solutions of the implicit differential equation
A(x)x'=g(x)
near points at which A is singular into solutions of the normal form
x1r x1' = +/-1,
x2' = ... = xn' = 0
near 0, and vice versa.
In particular, standard singular points in the sense of Rabier correspond to r = 1 in the above normal form.
A practical example leading to the normal form
with r = 2 is also given.
BibTeX entry:
@inproceedings{ReissigBoche98a,
author = {Gunther Rei{\ss}ig and Holger Boche},
title = {Straightening out trajectories near singular points of implicit differential equations},
booktitle = {Proc.~9th Int. Symp. System--Modelling--Control (SMC), Zakopane, Pl., } # apr # { 27--} # may # { 1},
year = 1998,
editor = {P. S. Szczepaniak},
isbn = {83-909161-0-X}
}
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