Premium
A novel approach to Lie group structured configuration spaces of rigid bodies
Author(s) -
Hante Stefan,
Arnold Martin
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710045
Subject(s) - quaternion , dual quaternion , configuration space , lie group , group (periodic table) , orientation (vector space) , rigid body , position (finance) , space (punctuation) , unit (ring theory) , rotation group so , mathematics , rotation (mathematics) , dual (grammatical number) , pure mathematics , geometry , algebra over a field , computer science , classical mechanics , physics , quantum mechanics , art , mathematics education , literature , finance , economics , operating system
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 ⋉ 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)