87 citations · 877 across the 97 of their papers we have counts for
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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: (…
The Euler-Poincare Equations and Semidirect Products with Applications to Continuum Theories
D. D. Holm, J. E. Marsden, T. S. Ratiu
We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Eul…
Dissipation Induced Instabilities
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden +1
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with sy…