Geodesic
Implicit quasilinear differential systems: A geometrical approach
Electronic journal of differential equations, Tome 1999 (1999)
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 $A({\bf x})\dot {\bf x} =\alpha ({\bf x})$ with $A({\bf x})$ 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.
Classification : 34C40, 57R25, 58A10, 58F99, 70Q05
Keywords: implicit differential equations, constrained systems, vector fields, differentiable manifolds 
@article{EJDE_1999__1999__a99,
     author = {Mu\~noz-Lecanda,  Miguel C. and Rom\'an-Roy,  N.},
     title = {Implicit quasilinear differential systems: {A} geometrical approach},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0930.34032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a99/}
}
TY  - JOUR
AU  - Muñoz-Lecanda,  Miguel C.
AU  - Román-Roy,  N.
TI  - Implicit quasilinear differential systems: A geometrical approach
JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
UR  - http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a99/
LA  - en
ID  - EJDE_1999__1999__a99
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%A Román-Roy,  N.
%T Implicit quasilinear differential systems: A geometrical approach
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a99/
%G en
%F EJDE_1999__1999__a99
Muñoz-Lecanda,  Miguel C.; Román-Roy,  N. Implicit quasilinear differential systems: A geometrical approach. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a99/