Journal of Geometry and Symmetry in Physics

In-Plane Oscillations of a Ring Driven by a Soap Film Catenoid

Pavel Grinfeld

Full-text: Open access

Abstract

In this paper, we calculate the frequency of small oscillations of a ring confined to a plane that, along with a fixed ring of the same size, supports a soap film catenoid. The restoring force is provided by the film's surface tension. We assume that the soap film is massless and continuously assumes the shape of minimal area. Mathematically, the problem is equivalent to calculating the second derivative of the total area with respect to the displacement of the ring. The calculus of moving surfaces is extensively used in the presented calculation.

Article information

Source
J. Geom. Symmetry Phys., Volume 20 (2010), 35-48.

Dates
First available in Project Euclid: 25 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495677845

Digital Object Identifier
doi:10.7546/jgsp-20-2010-35-48

Mathematical Reviews number (MathSciNet)
MR2780239

Zentralblatt MATH identifier
1216.53013

Citation

Grinfeld, Pavel. In-Plane Oscillations of a Ring Driven by a Soap Film Catenoid. J. Geom. Symmetry Phys. 20 (2010), 35--48. doi:10.7546/jgsp-20-2010-35-48. https://projecteuclid.org/euclid.jgsp/1495677845


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