arXiv subjects

Constantin Udriste

Publications and source records attributed to Constantin Udriste.

38 records · Page 3Linked to original sources

arXiv2000

Nonclassical Lagrangian Dynamics and Potential Maps

Section 1 refines the theory of harmonic and potential maps. Section 2 defines a generalized Lorentz world-force law and shows that any PDEs system of order one generates such a law in suitable geometrical structure. In other words, the solutions of any PDEs system of order one are harmonic or potential maps, if we use semi-Riemann-Lagrange structures. Section 3 formulates open problems regarding the geometry of semi-Riemann manifolds $(J^1(T,M), S_1)$, $(J^2(T,M), S_2)$, and shows that the Lorentz-Udriste world-force law is equivalent to covariant Hamilton PDEs on $(J^1(T,M), S_1)$.

math.DS↗

arXiv2000

Solutions of DEs and PDEs as Potential Maps Using First Order Lagrangians

Using parametrized curves (Section 1) or parametrized sheets (Section 3), and suitable metrics, we treat the jet bundle of order one as a semi-Riemann manifold. This point of view allows the description of solutions of DEs as pregeodesics (Section 1) and the solutions of PDEs as potential maps (Section 3), via Lagrangians of order one or via generalized Lorentz world-force laws. Implicitly, we solved a problem rised first by Poincaré: find a suitable geometric structure that converts the trajectories of a given vector field into geodesics (see also [6] - [11]). Section 2 and Section 3 realize the passage from the Lagrangian dynamics to the covariant Hamilton equations.

math.DS↗