Gross, Oliver and Pinkall, Ulrich and Wahl, Moritz (2025) Elastic Curves With Variable Bending Stiffness. STUDIES IN APPLIED MATHEMATICS, 155 (2): e70097. ISSN 0022-2526, 1467-9590
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We study stationary points of the bending energy of curves subject to constraints on the arc length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the arc length of the curve. Physically, this can be understood as a model for an elastic wire with isotropic cross section of varying thickness. We derive the corresponding Euler-Lagrange equations for variations that are compactly supported away from the endpoints thus obtaining characterizations for elastic curves with variable bending stiffness. Moreover, we provide a collection of alternative characterizations, for example, in terms of the curvature function. Adding to numerous known results relating elastic curves to dynamics, we explore connections between elastic curves with variable bending stiffness, variable length pendulums, and the flow of vortex filaments with finite thickness.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MINIMAL-SURFACES; DNA; CURVATURE; DYNAMICS; KNOTS; RODS; elastic curves; Euler-Lagrange equations; pendulum equation; variable bending stiffness; vortex filament flow |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Aug 2026 04:15 |
| Last Modified: | 12 Aug 2026 04:15 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66740 |
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