Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
A variational approach to a generalized elastica problem

C. Alex Safsten and Logan C. Tatham

Vol. 9 (2016), No. 3, 483–501
Abstract

In this paper, we apply the calculus of variations to solve the elastica problem. We examine a more general elastica problem in which the material under consideration need not be uniformly rigid. Using, the Euler–Lagrange equations, we derive a system of nonlinear differential equations whose solutions are given by these generalized elastica curves. We consider certain simplifying cases in which we can solve the system of differential equations. Finally, we use novel numerical techniques to approach solutions to the problem in full generality.

Keywords
calculus of variations, elastica, evolutionary algorithm, paper bending, Jacobi elliptic functions
Mathematical Subject Classification 2010
Primary: 49M30
Secondary: 49S05
Milestones
Received: 23 April 2015
Revised: 24 June 2015
Accepted: 1 July 2015
Published: 3 June 2016

Communicated by Frank Morgan
Authors
C. Alex Safsten
Mathematics Department
Brigham Young University
295 TMCB
Provo, UT 84602
United States
Logan C. Tatham
Mathematics Department
Brigham Young University
295 TMCB
Provo, UT 84602
United States