12 citations · 21 across the 5 of their papers we have counts for
5 papers
Dirac Reduction for Nonholonomic Mechanical Systems and Semidirect Products
François Gay-Balmaz, Hiroaki Yoshimura
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as…
Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions
François Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
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…
A new Lagrangian dynamic reduction in field theory
François Gay-Balmaz, Tudor S. Ratiu
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…
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 helicity and vorticity of liquid crystal flows
François Gay-Balmaz, Cesare Tronci
We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a mi…