On the geometry of the homogeneous representation for the group of proper rigid-body displacements
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.
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.
|Keywords||rigid-body displacements, birational transformations, kinematics|
|Journal||Romanian Journal of Technical Sciences - Applied Mechanics|
|Journal citation||58 (1-2), pp. 5 - 28|
|Publisher||Publishing House of the Romanian Academy|
|01 Jan 2013|
|Publication process dates|
|Deposited||10 Jun 2016|
|Accepted author manuscript|
CC BY-NC-ND 4.0
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