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8 papers · 1 filter
Energy methods in the stability problem for the free rigid body
Petre Birtea, Ioan Casu
For the free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each ca…
On the stability problem for the free rigid body
Ioan Casu
In the general case of the free rigid body we give a list of integrals of motion, which generate the set of Mishchenko's integrals. In the case of $\mathfrak{so}…
Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications
Feride Tiglay, Cornelia Vizman
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincaré eq…
Dual pairs in fluid dynamics
François Gay-Balmaz, Cornelia Vizman
This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the -dimensional Camassa-Holm (EPDiff) equation, including the proof…
The physical meaning of the de Sitter invariants
Ion I. Cotaescu
We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these represent…
Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups
François Gay-Balmaz, Cesare Tronci, Cornelia Vizman
We formulate Euler-Poincaré equations on the Lie group Aut(P) of automorphisms of a principal bundle P. The corresponding flows are referred to as EPAut flows. We mainly focus on g…