Discussion on: `Symmetry Reduction and Control of the Dynamics of a 2D Rigid Circular Cylinder and a Point Vortex. Vortex Capture and Scattering'

SEBASTIÁN J. FERRARO; DAVID MARTÍN DE DIEGO

EUROPEAN JOURNAL OF CONTROL

Año: 2007 vol. 13 p. 656 - 656

0947-3580

(No hay abstract ya que se trata de un "discussion paper" realizado por invitación, ver  Discussion section en http://www.elet.polimi.it/ejc/index.html. A continuación se  transcribe el abstract del artículo del cual este es una discusión.)Symmetry reduction and control of the Hamiltonian system of a 2D rigid circular  cylinder dynamically interacting with a point vortex external to it is presented. This  dynamic model is an idealized example in an inviscid framework of fully-coupled  solid-fluid systems interacting in the presence of vorticity and has potential applications  to problems in engineering and in nature involving the interaction of coherent vortices  with bodies moving (primarily) under their influence. The dynamics of the system  generically gives rise to two types of vortex orbits relative to the moving cylinder: bound and scattering orbits. The control input of a bounded external  force acting through the cylinder center-of-mass is then added. Exploiting the S^1-symmetry in the system, symplectic reduction is employed to formulate an  S^1-invariant control system, that preserves the momentum map, on the two-dimensional  symplectic reduced space. On this reduced space, both non-optimal and  optimal controllers, the latter using Pontryagin’s maximum principle, are  investigated with the control objective of changing the vortex orbit from a bound to a scattering type and vice versa.