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March 2021 Geodesics in the configuration spaces of two points in $\mathbb R^n$
Donald M. Davis
Tbilisi Math. J. 14(1): 149-162 (March 2021). DOI: 10.32513/tmj/19322008112

Abstract

We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs $(x,x')$ of points in $\mathbb R^n$ which satisfy $d(x,x')\ge \varepsilon$. We interpret this as two or three (depending on the parity of $n$) geodesic motion-planning rules for this configuration space. In the associated unordered configuration space, we need not prescribe that the points stay apart by $\varepsilon$. For this space, with a Euclidean-related metric, we show that geodesic motion-planning rules correspond to ordinary motion-planning rules on $RP^{n-1}$.

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Donald M. Davis. "Geodesics in the configuration spaces of two points in $\mathbb R^n$." Tbilisi Math. J. 14 (1) 149 - 162, March 2021. https://doi.org/10.32513/tmj/19322008112

Information

Received: 19 February 2020; Accepted: 14 February 2021; Published: March 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.32513/tmj/19322008112

Subjects:
Primary: 53C22
Secondary: 55M30, 55R80, 68T40

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 1 • March 2021
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