# Implicit Quasilinear Differential Systems: A Geometrical Approach

 dc.contributor.author Munoz-Lecanda, Miguel C. dc.contributor.author Roman-Roy, Narciso dc.date.accessioned 2019-11-22T14:39:10Z dc.date.available 2019-11-22T14:39:10Z dc.date.issued 1999-04-01 dc.description.abstract This work is devoted to the study of systems of implicit quasilinear differential equations. In general, no set of initial conditions is admissible for the system. It is shown how to obtain a vector field whose integral curves are the solution of the system, thus reducing the system to one that is ordinary. Using geometrical techniques, we give an algorithmic procedure in order to solve these problems for systems of the form A(x)ẋ = α(x) with A(x) being a singular matrix. As particular cases, we recover some results of Hamiltonian and Lagrangian Mechanics. In addition, a detailed study of the symmetries of these systems is carried out. This algorithm is applied to several examples arising from technical applications related to control theory. dc.description.department Mathematics dc.format Text dc.format.extent 33 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Munoz-Lecanda, M. C., & Roman-Roy, N. (1999). Implicit quasilinear differential systems: a geometrical approach. Electronic Journal of Differential Equations, 1999(10), pp. 1-33. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/8870 dc.language.iso en dc.publisher Southwest Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Implicit differential equations dc.subject Constrained systems dc.subject Vector fields dc.subject Differentiable manifolds dc.title Implicit Quasilinear Differential Systems: A Geometrical Approach dc.type Article

## Files

### Original bundle

Now showing 1 - 1 of 1
Name:
1999-Munoz-Lecanda-Roman-Roy.pdf
Size:
248.27 KB
Format:
Description: