dc.contributor.author Munoz-Lecanda, Miguel C. ( 0000-0002-7037-0248 ) dc.contributor.author Roman-Roy, Narciso ( 0000-0003-3663-9861 ) dc.date.accessioned 2019-11-22T14:39:10Z dc.date.available 2019-11-22T14:39:10Z dc.date.issued 1999-04-01 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. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/8870 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. en_US dc.format Text dc.format.extent 33 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Southwest Texas State University, Department of Mathematics en_US 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 en_US dc.subject Constrained systems en_US dc.subject Vector fields en_US dc.subject Differentiable manifolds en_US dc.title Implicit Quasilinear Differential Systems: A Geometrical Approach en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
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