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- W2949689312 abstract "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-Poincar'e 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 suitable constraints on the variations and by using invariance properties of the Lagrangian, as one does for the Euler equations for the rigid body and ideal fluids, we cast several standard Eulerian models of geophysical fluid dynamics (GFD) at various levels of approximation into Euler-Poincar'{e} form and discuss their corresponding Kelvin-Noether theorems and potential vorticity conservation laws." @default.
- W2949689312 created "2019-06-27" @default.
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- W2949689312 date "1999-03-25" @default.
- W2949689312 modified "2023-09-23" @default.
- W2949689312 title "The Euler-Poincare Equations in Geophysical Fluid Dynamics" @default.
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