Fibre derivatives: some applications to singular lagrangians
Xavier Gracia (Technical University of Catalonia)
TL;DR
This paper explores the fibre derivative in bundle maps, presenting constructions for singular lagrangians and applying them to solve Euler-Lagrange equations, with an example involving a free particle in curved space-time.
Contribution
It introduces new geometric constructions for singular lagrangians and demonstrates their application to solving Euler-Lagrange equations in complex settings.
Findings
Fibre derivatives provide useful tools for analyzing singular lagrangians.
A geometric method is developed to solve Euler-Lagrange equations.
Application to a free particle in curved space-time illustrates practical utility.
Abstract
The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric construction useful to solve the Euler-Lagrange equation of a singular lagrangian. A free particle in a curved space-time is studied as an example.
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