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Rigid body trajectories in different 6D spaces

Linton, C., Holderbaum, W. and Biggs, J. (2012) Rigid body trajectories in different 6D spaces. ISRN Mathematical Physics, 2012. Article ID: 467520. ISSN 2090-4681

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To link to this item DOI: 10.5402/2012/467520

Abstract/Summary

The objective of this paper is to show that the group 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Life Sciences > School of Biological Sciences > Department of Bio-Engineering
ID Code:32276
Publisher:Hindawi Publishing Corporation

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