Nonclassical Lagrangian Dynamics and Potential Maps

Details Nonclassical Lagrangian Dynamics and Potential Maps Nonclassical Lagrangian Dynamics and Potential Maps

2000-07-10

arxiv.org/abs/math/0007060v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

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 $(J^1(T,M), S_1)$.

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