Rotation Kinematics

  • Reza N. Jazar


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
$$ {}^Gr = Q_{Z,\alpha } {}^Br $$
$$ {}^Gr = \left[ {\begin{array}{*{20}c} X \\ Y \\ Z \\ \end{array} } \right] $$
$$ {}^Br = \left[ {\begin{array}{*{20}c} x \\ y \\ z \\ \end{array} } \right] $$
$$ Q_{Z,\alpha } = \left[ {\begin{array}{*{20}c} {\cos \alpha } & { - \sin \alpha } & 0 \\ {\sin \alpha } & {\cos \alpha } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]. $$


Rigid Body Coordinate Frame Rotation Matrix Euler Angle Local Frame 
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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

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

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