3 papers
math.SG2025
Infinite-dimensional Lagrange-Dirac systems with boundary energy flow I: Foundations
François Gay-Balmaz, Álvaro Rodríguez Abella, Hiroaki Yoshimura
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a l…
math.DG2023
Higher-order Euler-Poincaré field equations
Marco Castrillón López, Álvaro Rodríguez Abella
We develop a reduction theory for -invariant Lagrangian field theories defined on the higher-order jet bundle of a principal -bundle, thus obtaining the higher-order Euler-Po…
math-ph2023
Nonholonomic reduction for mechanical systems with collisions
Álvaro Rodríguez Abella, Leonardo J. Colombo
This paper studies nonsmooth variational problems on principal bundles for nonholonomic systems with collisions taking place in the boundary of the manifold configuration space of…