Vol. 9, No. 3, 2016

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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