Skip to main content
Article thumbnail
Location of Repository

Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds

By Francesco Bullo and Andrew D. Lewis

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. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.2307
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://motion.me.ucsb.edu/pdf/... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.