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Rigid Body Trajectories in Different 6D Spaces
Joint Authors
Biggs, James
Holderbaum, William
Linton, Carol
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-30
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Linton, Carol& Holderbaum, William& Biggs, James. 2012. Rigid Body Trajectories in Different 6D Spaces. ISRN Mathematical Physics،Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-473826
Modern Language Association (MLA)
Linton, Carol…[et al.]. Rigid Body Trajectories in Different 6D Spaces. ISRN Mathematical Physics No. 2012 (2012), pp.1-21.
https://search.emarefa.net/detail/BIM-473826
American Medical Association (AMA)
Linton, Carol& Holderbaum, William& Biggs, James. Rigid Body Trajectories in Different 6D Spaces. ISRN Mathematical Physics. 2012. Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-473826
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473826