576 citations · 1.9k across the 50 of their papers we have counts for
6 papers · 1 filter
Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures
Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok +1
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how St…
Covariant Balance Laws in Continua with Microstructure
Arash Yavari, Jerrold E. Marsden
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transforma…
A Discrete Theory of Connections on Principal Bundles
Melvin Leok, Jerrold E. Marsden, Alan D. Weinstein
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of co…
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…
Multisymplectic geometry, covariant Hamiltonians, and water waves
Jerrold E. Marsden, Steve Shkoller
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. In this theory, soluti…
Multisymplectic geometry, variational integrators, and nonlinear PDEs
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fund…