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math-ph2026
Dirac structures on tangent bundles: a geometric framework for variational principles, constrained dynamics, and symmetry reduction
Hiroaki Yoshimura
We introduce a Dirac structure on the tangent bundle of a configuration manifold, called a \textit{Lagrange--Dirac structure}, which is naturally induced by the Lagrangian two-form…
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…