First-order invariants of Euclidean motions

✍ Scribed by P. S. Donelan; C. G. Gibson

• Publisher: Springer Netherlands
• Year: 1991
• Tongue: English
• Weight: 985 KB
• Volume: 24
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00047045

✦ Synopsis

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.