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Rotation Kinematics

  • Reza N. Jazar

Abstract

Consider a rigid body B with a local coordinate frame Oxyz that is originally coincident with a global coordinate frame OXYZ. Point O of the body B is fixed to the ground G and is the origin of both coordinate frames. If the rigid body B rotates a degrees about the Z-axis of the global coordinate frame, then coordinates of any point P of the rigid body in the local and global coordinate frames are related by the following equation
$$ {}^Gr = Q_{Z,\alpha } {}^Br $$
(2.1)
where
$$ {}^Gr = \left[ {\begin{array}{*{20}c} X \\ Y \\ Z \\ \end{array} } \right] $$
(2.2)
$$ {}^Br = \left[ {\begin{array}{*{20}c} x \\ y \\ z \\ \end{array} } \right] $$
(2.3)
and
$$ Q_{Z,\alpha } = \left[ {\begin{array}{*{20}c} {\cos \alpha } & { - \sin \alpha } & 0 \\ {\sin \alpha } & {\cos \alpha } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]. $$
(2.4)

Keywords

Rigid Body Coordinate Frame Rotation Matrix Euler Angle Local Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Reza N. Jazar
    • 1
  1. 1.Department of Mechanical EngineeringManhattan CollegeRiverdale

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