A geometric and variational setting for nonholonomic mechanics

11 aprile 2016
Versione stampabile

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 11:00

Relatore:

  • Olga Rossi (The University of Ostrava, Czech Republic - La Trobe University Melbourne, Australia )

Abstract:
The aim of nonholonomic mechanics is to study dynamics, symmetries, conservation laws and other properties of particles and bodies subject to constraints in the form of a system of first order differential equations.
We shall present a geometric setting where the constraint manifold naturally arises as a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. This model allows to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. 
It applies to general (possibly nonconservative) mechanical systems subject to general (possibly nonlinear) nonholonomic constraints, and admits a straightforward generalization to higher order mechanics and to field theory. 
In particular, we are concerned with the following topics: the geometry of nonholonomic constraints, equations of motion of nonholonomic systems on constraint manifolds, nonholonomic variational principle, symmetries, nonholonomic Noether theorem, regularity and nonholonomic Hamilton equations.

Referente: Enrico Pagani