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. <i>Electronic Journal of Differential Equations, 1999</i>(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 |