Personne

Tudor Ratiu

Publications associées (105)

Dirac Structures, Nonholonomic Systems And Reduction

The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail. ...

Elsevier2012

Euler-Poincare Approaches to Nematodynamics

Tudor Ratiu, François Gay-Balmaz, Cesare Tronci

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincar, reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen's micropolar theory. In particular, we sho ...

Springer Netherlands2012

Higher order Lagrange-Poincar, and Hamilton-Poincar, reductions

Tudor Ratiu, François Gay-Balmaz

Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular, we obtain the r ...

2011

Geometry of nonabelian charged fluids

Tudor Ratiu, François Gay-Balmaz

The goal of this paper is to derive the Hamiltonian structure of polarized and magnetized Euler-Maxwell fluids by reduction of the canonical symplectic form on phase space, and to generalize the dynamics to the nonabelian case. The Hamiltonian function we ...

2011

Induced Dirac structures on isotropy-type manifolds

Tudor Ratiu, Madeleine Jotz

A new method of singular reduction is extended from Poisson to Dirac manifolds. Then it is shown that the Dirac structures on the strata of the quotient coincide with those of the only other known singular Dirac reduction method. ...

Birkhäuser-Verlag, Springer2011

The Momentum Map Representation of Images

Tudor Ratiu, François Gay-Balmaz, Martins Bruveris

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a ...

Springer Verlag2011

Flexible beam in R3 under large overall motions and Asynchronous Variational Integrators

Tudor Ratiu, François Gay-Balmaz, Yves Weinand, François Marie Alain Demoures

The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...

IABSE ETH Zurich2011

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

Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about G-invariant vector fields and one-forms are shown. ...

2011

Invariant generators for generalized distributions

Tudor Ratiu, Madeleine Jotz

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

Obituary: Jerry Marsden

Tudor Ratiu

2011

Remembering Jerry Marsden IN MEMORIAM

Tudor Ratiu

SP MAIK Nauka/Interperiodica, Springer2010

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

A Class of Integrable Flows on the Space of Symmetric Matrices

Tudor Ratiu

For a given skew symmetric real n x n matrix N, the bracket X, Y = XNY - YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n x n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to inves ...

Springer Verlag2009

The Momentum Map In Poisson Geometry

Juan-Pablo Ortega, Tudor Ratiu

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction. ...

2009

Openness And Convexity For Momentum Maps

Juan-Pablo Ortega, Tudor Ratiu

The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of a topological nature; more specifically, we show that convexity follows if the map is open onto its image and ha ...

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

Poisson Reduction by Distributions

Tudor Ratiu, Madeleine Jotz

It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail. ...

Springer Verlag2009