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On the Hierarchy of screw systems

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Abstract

LetE(3) be the Lie group of proper rigid motions of Euclidean 3-space. The adjoint action ofE(3) on its Lie algebrae(3) induces an action on the Grassmannian of subspaces of given dimensiond. Projectively, these subspaces are the screw systems of classical kinematics. The authors show that existing classifications of screw systems give rise to Whitney regular stratifications of the Grassmannians, and establish diagrams of specialisations for the strata. A list is given of the screw systems which can appear generically for motions of 3-space with at most three degrees of freedom.

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Authors and Affiliations

  1. Department of Mathematics, Victoria University of Wellington, PO Box 600, Wellington, New Zealand

    P. S. Donelan

  2. Department of Pure Mathematics, University of Liverpool, Liverpool L69 3BX, PO Box 147, England

    C. G. Gibson

Authors
  1. P. S. Donelan
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  2. C. G. Gibson
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Donelan, P.S., Gibson, C.G. On the Hierarchy of screw systems. Acta Appl Math 32, 267–296 (1993). https://doi.org/10.1007/BF01082452

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