Per citar aquest document: http://ddd.uab.cat/record/44186
Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds
Bullo, Francesco
Lewis, Andrew D.
Centre de Recerca Matemàtica

Publicació: Centre de Recerca Matemàtica 2005
Col·lecció: Prepublicacions del Centre de Recerca Matemàtica ; 618
Resum: 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.
Drets: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Llengua: Anglès.
Document: preprint
Matèria: Riemann, Varietats de

Adreça alternativa: http://hdl.handle.net/2072/2156


52 p, 4.3 MB

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