576 citations · 1.9k across the 50 of their papers we have counts for
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Discrete Euler-Poincaré and Lie-Poisson Equations
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
In this paper, discrete analogues of Euler-Poincaré and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups with Lagrangians $L:TG \to {\mat…
The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
J. E. Marsden, T. S. Ratiu, S. Shkoller
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-pr…
Lagrangian Reduction, the Euler--Poincaré Equations, and Semidirect Products
H. Cendra, D. D. Holm, J. E. Marsden +1
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which ar…
A Nonlinear Analysis of the Averaged Euler Equations
Darryl D. Holm, Shinar Kouranbaeva, Jerrold E. Marsden +2
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with…
The Euler-Poincare Equations in Geophysical Fluid Dynamics
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
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: (…