On the geometry of the homogeneous representation for the group of proper rigid-body displacements

Journal article

Selig, JM (2013). On the geometry of the homogeneous representation for the group of proper rigid-body displacements. Romanian Journal of Technical Sciences - Applied Mechanics. 58 (1-2), pp. 5 - 28.
AuthorsSelig, JM
Abstract

This work investigates the geometry of the homogeneous representation of the group of proper rigid-body displacements. In particular it is shown that there is a birational transformation from the Study quadric to the variety determined by the homogeneous representation. This variety is shown to be the join of a Veronese variety with a 2-plane. The rest of the paper looks at sub-varieties, first those which are sub-groups of the displacement group and then some examples defined by geometric constraints. In many cases the varieties are familiar as sub-varieties of the Study quadric, here their transforms to the homogeneous representation is considered. A final section deals with the map which sends each displacements to its inverse. This is shown to be a quadratic birational transformation.

Keywordsrigid-body displacements, birational transformations, kinematics
Year2013
JournalRomanian Journal of Technical Sciences - Applied Mechanics
Journal citation58 (1-2), pp. 5 - 28
PublisherPublishing House of the Romanian Academy
ISSN0035-4074
Publication dates
Print01 Jan 2013
Publication process dates
Deposited10 Jun 2016
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