184 citations · 413 across the 5 of their papers we have counts for
5 papers
Abstract mechanical connection and Abelian reconstruction for almost Kahler manifolds
Sergey Pekarsky, Anthony D. Blaom, Jerrold E. Marsden
When the phase space P of a Hamiltonian G-system (P, ω, G, J, H) has an almost Kahler structure a preferred connection, called abstract mechanical connection, can be defined by dec…
On the stability of periodic 2D Euler-alpha flows
Sergey Pekarsky, Steve Shkoller
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wav…
Variational methods, multisymplectic geometry and continuum mechanics
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller +1
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general f…
Symmetry reduction of discrete Lagrangian mechanics on Lie groups
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
For a discrete mechanical system on a Lie group determined by a (reduced) Lagrangian we define a Poisson structure via the pull-back of the Lie-Poisson structure on the…
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…