Rigid body trajectories in different 6D spaces
type: Item
instance of: scholarly article
title: Rigid body trajectories in different 6D spaces
zbMATH Open document ID: 1360.70004
DOI: 10.5402/2012/467520
author: Carol Linton
author: William Holderbaum
author: James Biggs
published in: ISRN Mathematical Physics
publication date: 2012-10-08T00:00:00Z
review text: Summary: The objective of this paper is to show that the group \(\mathrm{SE}(3)\) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.
Mathematics Subject Classification ID: 70B10
zbMATH DE Number: 6092161
Wikidata QID: Q58690507
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/467520
OpenAlex ID: W2118846159
cites work: Q5458620
cites work: Q2999582
cites work: Q4423258
cites work: Q4335551
cites work: Geometric Mechanics
cites work: Discrete Geometry for Computer Imagery
cites work: Geometric Fundamentals of Robotics
description: scientific article; zbMATH DE number 6092161