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François Gay-Balmaz

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Related publications (34)

Clebsch Optimal Control Formulation In Mechanics

Tudor Ratiu, François Gay-Balmaz

This paper introduces and studies a class of optimal control problems based on the Clebsch approach to Euler-Poincare dynamics. This approach unifies and generalizes a wide range of examples appearing in the literature: the symmetric formulation of N-dimen ...

2011

Lagrange-Poincare field equations

Tudor Ratiu, François Gay-Balmaz

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original ...

2011

Reduction theory for symmetry breaking with applications to nematic systems

François Gay-Balmaz, Cesare Tronci

We formulate Euler-Poincare and Lagrange-Poincare equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. Th ...

2010

Symmetry Reduced Dynamics of Charged Molecular Strands

Tudor Ratiu, François Gay-Balmaz

The equations of motion are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that these equations are nonloca ...

Springer-Verlag2010

A New Lagrangian Dynamic Reduction In Field Theory

Tudor Ratiu, François Gay-Balmaz

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a ...

2010

On the classification of the coadjoint orbits of the Sobolev Bott-Virasoro group

François Gay-Balmaz

The purpose of this paper is to give the classification of the Bott-Virasoro coadjoint orbits, with nonzero central charge, in the functional analytic setting of smooth Hilbert manifolds. The central object of the paper is thus the completion of the Bott-V ...

2009

The geometric structure of complex fluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microf ...

Elsevier2009

Infinite dimensional geodesic flows and the universal Teichmüller space

François Gay-Balmaz

The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...

EPFL2009

Variational Principles For Spin Systems And The Kirchhoff Rod

Tudor Ratiu, François Gay-Balmaz

We obtain the affine Euler-Poincare equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's ...

2009

Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations

Tudor Ratiu, François Gay-Balmaz

The problem treated here is to find the Hamiltonian structure for an ideal gauge-charged fluid. Using a Kaluza-Klein point of view, we obtain the non-canonical Poisson bracket and the motion equations by a Poisson reduction involving the automorphism group ...

American Mathematical Society, P.O. Box 6248 Ms. Phoebe Murdock, Providence, Ri 02940 Usa2008

Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids

Tudor Ratiu, François Gay-Balmaz

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bun ...

2008

Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of ...

2008

Group actions on chains of Banach manifolds and applications to fluid dynamics

Tudor Ratiu, François Gay-Balmaz

2007

The Lie-Poisson structure of the LAE-$\alpha$ equation

Tudor Ratiu, François Gay-Balmaz

2005

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