Implicit Quasilinear Differential Systems: A Geometrical Approach
Date
1999-04-01
Authors
Munoz-Lecanda, Miguel C.
Roman-Roy, Narciso
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Implicit differential equations, Constrained systems, Vector fields, Differentiable manifolds
Citation
Munoz-Lecanda, M. C., & Roman-Roy, N. (1999). Implicit quasilinear differential systems: a geometrical approach. <i>Electronic Journal of Differential Equations, 1999</i>(10), pp. 1-33.
Rights
Attribution 4.0 International