Rigid Motions and Congruence

1979 ◽  
pp. 210-219
Author(s):  
J. A. Thorpe
Keyword(s):  
Rigid Motions

scholarly journals Maximizing the overlap of two planar convex sets under rigid motions

2007 ◽  
Vol 37 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Hee-Kap Ahn ◽  
Otfried Cheong ◽  
Chong-Dae Park ◽  
Chan-Su Shin ◽  
Antoine Vigneron
Keyword(s):  
Convex Sets ◽  
Planar Convex ◽  
Rigid Motions

Rigid motions relative to an observer:L-rigidity

1996 ◽  
Vol 35 (7) ◽  
pp. 1511-1522 ◽  
Author(s):  
M. Barreda ◽  
J. Olivert
Keyword(s):  
Rigid Motions

scholarly journals Rigid motions and generalized Newtonian gravitation

2013 ◽  
Vol 45 (8) ◽  
pp. 1531-1546 ◽  
Author(s):  
Xavier Jaén ◽  
Alfred Molina
Keyword(s):  
Newtonian Gravitation ◽  
Rigid Motions

Rigid Motions as Matrices

2021 ◽  
pp. 243-252
Author(s):  
Kristopher Tapp
Keyword(s):  
Rigid Motions

scholarly journals Remarks on the self-shrinking Clifford torus

2020 ◽  
Vol 2020 (765) ◽  
pp. 139-170
Author(s):  
Christopher G. Evans ◽  
Jason D. Lotay ◽  
Felix Schulze
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
The Self ◽  
The Other ◽  
Local Entropy ◽  
Clifford Torus ◽  
Infinitesimal Deformations ◽  
Rigid Motions ◽  
The One

AbstractOn the one hand, we prove that the Clifford torus in {\mathbb{C}^{2}} is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian F-stable and locally area minimising under Hamiltonian variations. On the other hand, we show that the Clifford torus is rigid: it is locally unique as a self-shrinker for mean curvature flow, despite having infinitesimal deformations which do not arise from rigid motions. The proofs rely on analysing higher order phenomena: specifically, showing that the Clifford torus is not a local entropy minimiser even under Hamiltonian variations, and demonstrating that infinitesimal deformations which do not generate rigid motions are genuinely obstructed.

scholarly journals A Bi-Invariant Statistical Model Parametrized by Mean and Covariance on Rigid Motions

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 432
Author(s):  
Emmanuel Chevallier ◽  
Nicolas Guigui
Keyword(s):  
Statistical Model ◽  
Convergence Rates ◽  
Probability Distributions ◽  
Exponential Map ◽  
Jacobian Determinant ◽  
Numerical Comparison ◽  
Rigid Motions ◽  
Invariant Statistics ◽  
The Moment ◽  
Explicit Expressions

This paper aims to describe a statistical model of wrapped densities for bi-invariant statistics on the group of rigid motions of a Euclidean space. Probability distributions on the group are constructed from distributions on tangent spaces and pushed to the group by the exponential map. We provide an expression of the Jacobian determinant of the exponential map of S E ( n ) which enables the obtaining of explicit expressions of the densities on the group. Besides having explicit expressions, the strengths of this statistical model are that densities are parametrized by their moments and are easy to sample from. Unfortunately, we are not able to provide convergence rates for density estimation. We provide instead a numerical comparison between the moment-matching estimators on S E ( 2 ) and R 3 , which shows similar behaviors.

Stability of rigid motions and rollers in bicomponent flows of immiscible liquids

1985 ◽  
Vol 153 (-1) ◽  
pp. 151 ◽  
Author(s):  
Daniel D. Joseph ◽  
Y. Renardy ◽  
M. Renardy ◽  
K. Nguyen
Keyword(s):  
Immiscible Liquids ◽  
Rigid Motions
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