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math-ph2025
Euler--Poincaré reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics
Yusuke Ono, Simone Fiori, Linyu Peng
The Euler--Poincaré equations, firstly introduced by Henri Poincaré in 1901, arise from the application of Lagrangian mechanics to systems on Lie groups that exhibit symmetries,…
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…