The Euler – Poincaré Equations in Geophysical Fluid Dynamics

@inproceedings{Holm1998TheE,
  title={The Euler – Poincar{\'e} Equations in Geophysical Fluid Dynamics},
  author={Darryl D. Holm and Tudor S. Ratiu},
  year={1998}
}
Recent theoretical work has developed the Hamilton’s-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: 1. Euler–Poincaré equations (the Lagrangian analog of Lie-Poisson Hamiltonian equations) are derived for a parameter dependent Lagrangian from a general variational principle of Lagrange d’Alembert type in which variations are constrained; 2. an abstract Kelvin–Noether theorem is derived for such systems. By imposing… CONTINUE READING
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