The authors derive discrete Euler-Poincaré equations on Lie groups with advected parameters, extend the continuous and discrete Kelvin-Noether theorems, and demonstrate the approach on underwater vehicle dynamics via numerical simulations.
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Euler--Poincar\'e reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics
The authors derive discrete Euler-Poincaré equations on Lie groups with advected parameters, extend the continuous and discrete Kelvin-Noether theorems, and demonstrate the approach on underwater vehicle dynamics via numerical simulations.