Seminario Geometría, Mecánica y Control
Variational Integrators for Time-Dependent Mechanical Systems on Lie Groups: Error Analysis and Long-Time Behavior
Ponente: Leonardo Colombo (Centro de Automática y Robótica (CSIC-UPM))Fecha: viernes 30 de octubre de 2026 - 13:00 (Madrid time) and 12:00 (La Laguna time)Lugar: Aula Gris 3, ICMAT
Online: TBA
Resumen:
We develop a variational framework for time-dependent Lagrangian systems on Lie groups, combining geometric discretization, symmetry reduction, and structure-preserving numerical integration. Particular attention is devoted to the error analysis of variational integrators, and to the convergence properties of retraction-based schemes.
We then investigate the long-time behavior of these integrators through backward error analysis on the extended phase space, establishing the affine structure of the modified Hamiltonian and exponentially accurate estimates under suitable analyticity assumptions. The theoretical results are illustrated by a time-dependent rigid body and a mechanical attitude-consensus problem on (SO(3)^N), highlighting discrete momentum preservation and long-time numerical behavior.
This is a joint work with Emma Eyrea Irazú, David Martín de Diego, Daniela Sánchez and Marcela Zuccalli.
