Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/8101
Title: | Rolling Maps in Riemannian Manifolds | Contributor(s): | Krakowski, Krzysztof (author); Silva Leite, Fatima (author) | Publication Date: | 2010 | Handle Link: | https://hdl.handle.net/1959.11/8101 | Abstract: | We study rolling of one submanifold upon another submanifold, both isometrically embedded in a Riemannian manifold.We generalise the definition of rolling in Sharpe (1997). In this new definition, the Euclidean group of motions is replaced by the Lie group of orientation preserving isometries. We show that rolling in this general situation is unique. We prove a theorem that enables us to learn how to roll non-Euclidean manifolds that result from deformations of Euclidean submanifolds from the knowledge of the kinematic equations of rolling these Euclidean submanifolds. Taking into account that the ellipsoid is a deformed sphere, we apply the above mentioned theorem and the kinematic equations for the rolling sphere to derive the kinematic equations for rolling the ellipsoid. This example serves as a motivation to roll other manifolds. | Publication Type: | Conference Publication | Conference Details: | CONTROLO 2010: 9th Portuguese Conference on Automatic Control, Coimbra, Portugal, 8th - 10th September, 2010 | Source of Publication: | Proceedings of the 9th Portuguese Conference on Automatic Control (CONTROLO'2010), p. 456-461 | Publisher: | Universidade de Coimbra, Faculdade de Ciências e Tecnologia | Place of Publication: | Coimbra, Portugal | Fields of Research (FoR) 2008: | 010203 Calculus of Variations, Systems Theory and Control Theory 010102 Algebraic and Differential Geometry |
Socio-Economic Objective (SEO) 2008: | 970109 Expanding Knowledge in Engineering 970101 Expanding Knowledge in the Mathematical Sciences |
HERDC Category Description: | E2 Non-Refereed Scholarly Conference Publication | Publisher/associated links: | http://mcs.une.edu.au/~kris/ http://www.controlo2010.org/ |
---|---|
Appears in Collections: | Conference Publication |
Files in This Item:
File | Description | Size | Format |
---|
Page view(s)
1,124
checked on Jun 23, 2024
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.