Rigid body trajectories in different 6D spaces

Linton, C; Holderbaum, W; Biggs, J

Abstract

The objective of this paper is to show that the group SE3 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.

Citation

Linton, C., Holderbaum, W., & Biggs, J. (2012). Rigid body trajectories in different 6D spaces. International Scholarly Research Notices, 2012, 467520. https://doi.org/10.5402/2012/467520

• Journal Article Type: Article
• Acceptance Date: Jun 4, 2012
• Publication Date: Jul 30, 2012
• Deposit Date: Dec 17, 2021
• Publicly Available Date: Dec 17, 2021
• Journal: ISRN Mathematical Physics
• Publisher: Hindawi
• Volume: 2012
• Pages: 467520
• DOI: https://doi.org/10.5402/2012/467520
• Publisher URL: https://doi.org/10.5402/2012/467520
• Related Public URLs: https://www.hindawi.com/journals/isrn/