Queen's University - Utility Bar

QSpace at Queen's University >
Mathematics and Statistics >
Andrew D. Lewis >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1974/211

Title: Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
Authors: Bullo, Francesco
Lewis, Andrew D.

Files in This Item:

File Description SizeFormat
2004f_letter.pdf4.52 MBAdobe PDFView/Open
Issue Date: 2004
Abstract: Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory ``commute.'' As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.
URI: http://hdl.handle.net/1974/211
Appears in Collections:Andrew D. Lewis

Items in QSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

  DSpace Software Copyright © 2002-2008  The DSpace Foundation - TOP