3 papers
math.SG2025
Infinite-dimensional Lagrange-Dirac systems with boundary energy flow II: Field theories with bundle-valued forms
François Gay-Balmaz, Álvaro Rodríguez Abella, Hiroaki Yoshimura
Part I of this paper introduced the infinite dimensional Lagrange-Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This ap…
math.SG2025
Infinite-dimensional Lagrange-Dirac systems with boundary energy flow I: Foundations
François Gay-Balmaz, Álvaro Rodríguez Abella, Hiroaki Yoshimura
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a l…
math-ph2024
Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanics
Linyu Peng, Hiroaki Yoshimura
In this paper, we propose the concept of -discrete Dirac structures over a manifold, where we define -discrete two-forms on the manifold and incorporate discrete cons…