A bridge between Willmore–Chen submanifolds and elastic curves

2001 ◽  
Vol 47 (8) ◽  
pp. 5145-5156 ◽  
Author(s):  
Jose L. Cabrerizo
Keyword(s):  
Elastic Curves

scholarly journals Curve straightening and a minimax argument for closed elastic curves

Topology ◽  
1985 ◽  
Vol 24 (1) ◽  
pp. 75-88 ◽  
Author(s):  
Joel Langer ◽  
David A. Singer
Keyword(s):  
Elastic Curves

The design space of plane elastic curves

2021 ◽  
Vol 40 (4) ◽  
pp. 1-20
Author(s):  
Christian Hafner ◽  
Bernd Bickel
Keyword(s):  
Design Space ◽  
Elastic Curves

Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2

2018 ◽  
Vol 3 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Chun-Chi Lin ◽  
Yang-Kai Lue
Keyword(s):  
Evolution Equation ◽  
Convergent Subsequence ◽  
Second Order ◽  
Plane Curves ◽  
Smooth Solutions ◽  
Fixed Position ◽  
Elastic Curves ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Abstract For any given C2-smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.

scholarly journals Shape Analysis of Elastic Curves in Euclidean Spaces

2011 ◽  
Vol 33 (7) ◽  
pp. 1415-1428 ◽  
Author(s):  
A Srivastava ◽  
E Klassen ◽  
S H Joshi ◽  
I H Jermyn
Keyword(s):  
Shape Analysis ◽  
Euclidean Spaces ◽  
Elastic Curves

scholarly journals Confined Elastic Curves

2011 ◽  
Vol 71 (6) ◽  
pp. 2205-2226 ◽  
Author(s):  
Patrick W. Dondl ◽  
Luca Mugnai ◽  
Matthias Röger
Keyword(s):  
Elastic Curves

On Shape of Plane Elastic Curves

2006 ◽  
Vol 73 (3) ◽  
pp. 307-324 ◽  
Author(s):  
Washington Mio ◽  
Anuj Srivastava ◽  
Shantanu Joshi
Keyword(s):  
Elastic Curves

TRANSFORMATIONS OF A SPACE CURVE AND APPLICATIONS TO ELASTIC CURVES

2018 ◽  
Vol 21 (2) ◽  
pp. 119-140
Author(s):  
Vishesh S. Bhat ◽  
R. Hari Baskar
Keyword(s):  
Space Curve ◽  
Elastic Curves

The Elastica With End-Load Flip-Over

1988 ◽  
Vol 55 (4) ◽  
pp. 845-848 ◽  
Author(s):  
J. F. Wilson ◽  
J. M. Snyder
Keyword(s):  
Cantilever Beam ◽  
Abrupt Change ◽  
Robotic Manipulators ◽  
Finite Deformations ◽  
Follower Load ◽  
System Parameters ◽  
Small Increment ◽  
Elastic Curves ◽  
Manipulator Arm

A high flexure manipulator arm is modeled as an elastic cantilever beam with a tip payload and an eccentric tip follower load that drives the arm. Shapes of the resulting elastic curves for finite deformations (the elastica) are calculated in terms of nondimensional system parameters. For critical combinations of these parameters, a small increment in the driving follower load causes an abrupt change in the shape of the elastica. The abrupt change in tip angle is typically of the order of π radians. These results are applicable to the design of high flexure robotic manipulators.

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