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,…