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The Study Quadric

  • J. M. Selig
Part of the Monographs in Computer Science book series (MCS)

Abstract

It was probably Study who first considered the possible positions of a rigid body as points in a non-Euclidian space; see Study [87]. His idea was to specify the position of the body by attaching a coordinate frame to it. He called these ‘points’ soma, which is Greek for body. Clifford’s biquaternions were then used as coordinates for the space. As we saw in section 9.3, using the biquaternion representation, the elements of the group of rigid body motions can be thought of as the points of a six-dimensional projective quadric (excluding a 3-plane of ‘ideal’ points). If we fix a particular position of the rigid body as the home position, then all other positions of the body can be described by the unique transformation that takes the home configuration to the present one. In this way, we see that Study’s somas are just the points of the six-dimensional projective quadric the Study quadric, (not forgetting to exclude the points on the special 3-plane).

Keywords

Isotropy Group Base Point Group Element Homology Class Revolute Joint 
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 New York 1996

Authors and Affiliations

  • J. M. Selig
    • 1
  1. 1.School of Electrical, Electronic, and Information EngineeringSouth Bank UniversityLondonUK

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