Rigid body trajectories in different 6D spaces

Carol Linton, William Holderbaum, James Biggs

Research output: Contribution to journalArticle

Abstract

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 tend to zero as the scaling factor increases. The semi-direct 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.
LanguageEnglish
Article number467520
Number of pages21
JournalISRN Mathematical Physics
Volume2012
Early online date4 Jun 2012
DOIs
Publication statusPublished - Jul 2012

Fingerprint

Rigid Body
Trajectories
Trajectory
Semi-direct product
Symmetry
Moment of inertia
Scaling Factor
Poisson Structure
Hyperbolic Space
Euclidean space
Scaling
Tend
Motion
Zero

Keywords

  • Rigid body trajectories
  • semi-direct product of translations and rotations
  • structure constants and equations of motion equations
  • imposed Lie-Poisson structure on Special Euclidean group

Cite this

Linton, Carol ; Holderbaum, William ; Biggs, James. / Rigid body trajectories in different 6D spaces. In: ISRN Mathematical Physics. 2012 ; Vol. 2012.
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Rigid body trajectories in different 6D spaces. / Linton, Carol; Holderbaum, William; Biggs, James.

In: ISRN Mathematical Physics, Vol. 2012, 467520, 07.2012.

Research output: Contribution to journalArticle

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