Open Access Te Herenga Waka-Victoria University of Wellington
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Polynomial Invariants of the Euclidean Group Action on Multiple Screws

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posted on 2021-11-10, 03:59 authored by Crook, Deborah

In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.


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Te Herenga Waka—Victoria University of Wellington

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Te Herenga Waka—Victoria University of Wellington

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Master of Science

Victoria University of Wellington Item Type

Awarded Research Masters Thesis



Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research


Donelan, Peter