Acta Applicandae Mathematica

, Volume 24, Issue 3, pp 233–251 | Cite as

First-order invariants of Euclidean motions

  • P. S. Donelan
  • C. G. Gibson


Let E(n) be the lie group of proper rigid motions of Euclidean n-space. The paper is concerned with the adjoint action of E(n) on its Lie algebra e(n), and the induced action on the Grassmannian of subspaces of e(n) of a given dimension. For the adjoint action, the authors list explicit generators for the ring of invariant polynomials. In the case n=3, of greatest physical interest, explicit finite invariant stratifications are given for the Grassmannians, providing a formal listing of the screw-systems familiar in theoretical kinematics.

AMS subject classification (1991)


Key words

Kinematics invariants screws 


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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • P. S. Donelan
    • 1
  • C. G. Gibson
    • 2
  1. 1.Department of MathematicsVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Department of Pure MathematicsUniversity of LiverpoolLiverpoolEngland

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