A novel approach to Lie group structured configuration spaces of rigid bodies. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Hante, Stefan; Arnold, Martin
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 151
• Page End: 152
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710045
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In rigid body mechanics, a body's configuration consisting of orientation and position have to be described, as well as angular velocity and velocity. There are several different ways to do this, leading to different configuration spaces. Popular choices include SO(3) × ℝ 3, SE(3) or unit dual quaternions. All these configuration spaces possess a Lie group structure. We present the novel approach 𝕊 ⋉ ℝ 3, which is a configuration space similar to SE(3), but describes the orientation in terms of unit quaternions instead of rotation matrices. Furthermore we show its relation to and advantages over other configuration spaces. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)