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Rigid body trajectories in different 6D spaces

Linton, Carol and Holderbaum, William and Biggs, James (2012) Rigid body trajectories in different 6D spaces. ISRN Mathematical Physics, 2012. ISSN 2090-4673

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    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.

    Item type: Article
    ID code: 39984
    Notes: Open Journal - Copyright owned by Authors
    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 , Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Mathematics, Aerospace Engineering, Control and Systems Engineering, Analysis
    Subjects: Technology > Mechanical engineering and machinery
    Technology > Motor vehicles. Aeronautics. Astronautics
    Science > Mathematics
    Department: Faculty of Engineering > Mechanical and Aerospace Engineering
    Technology and Innovation Centre > Advanced Engineering and Manufacturing
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    Depositing user: Pure Administrator
    Date Deposited: 11 Jun 2012 16:16
    Last modified: 30 May 2014 19:05
    URI: http://strathprints.strath.ac.uk/id/eprint/39984

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