A differential geometric setting for mixed first- and second-order ordinary differential equations
| Autor: | Dj Saunders, Frans Cantrijn, Willy Sarlet |
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| Rok vydání: | 1997 |
| Předmět: |
Mathematical analysis
General Physics and Astronomy Statistical and Nonlinear Physics Time-scale calculus Delay differential equation Integrating factor Examples of differential equations Stochastic partial differential equation Collocation method Applied mathematics Differential algebraic equation Mathematical Physics Mathematics Numerical partial differential equations |
| Zdroj: | Journal of Physics A: Mathematical and General. 30:4031-4052 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/30/11/029 |
| Popis: | A geometrical framework is presented for modelling general systems of mixed first- and second-order ordinary differential equations. In contrast to our earlier work on non-holonomic systems, the first-order equations are not regarded here as a priori given constraints. Two nonlinear (parametrized) connections appear in the present framework in a symmetrical way and they induce a third connection via a suitable fibred product. The space where solution curves of the given differential equations live, singles out a specific projection among the many fibrations in the general picture. A large part of the paper is about the development of intrinsic tools - tensor fields and derivations - for an adapted calculus along . A major issue concerns the extent to which the usual construction of a linear connection associated with second-order equations fails to work in the presence of coupled first-order equations. An application of the ensuing calculus is presented. |
| Databáze: | OpenAIRE |
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