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A variational
approach to a generalized elastica problem
C. Alex Safsten and Logan C. Tatham
Vol. 9 (2016), No. 3, 483–501
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 49M30
Secondary: 49S05
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Milestones
Received: 23 April 2015
Revised: 24 June 2015
Accepted: 1 July 2015
Published: 3 June 2016
Communicated by Frank Morgan
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Authors |
| C. Alex Safsten | |
| Mathematics Department Brigham Young University 295 TMCB Provo, UT 84602 United States |
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| Logan C. Tatham | |
| Mathematics Department Brigham Young University 295 TMCB Provo, UT 84602 United States |
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