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Physics > Classical Physics

arXiv:2204.08991 (physics)
[Submitted on 18 Apr 2022 (v1), last revised 27 Oct 2022 (this version, v2)]

Title:Mathematics of Floating 3D Printed Objects

Authors:Daniel M. Anderson, Brandon G. Barreto-Rosa, Joshua D. Calvano, Lujain Nsair, Evelyn Sander
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Abstract:We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating shapes with two-dimensional cross sections and identify analytically and/or computationally a potential energy landscape that helps identify stable and unstable floating orientations. We compare our analyses and computations to experiments on floating objects designed and created through 3D printing. In addition to our results, we provide code for testing the floating configurations for new shapes, as well as giving details of the methods for 3D printing the objects. The paper includes conjectures and open problems for further study.
Comments: 31 pages, 17 figures
Subjects: Classical Physics (physics.class-ph); Dynamical Systems (math.DS)
MSC classes: Primary 54C40, 14E20, Secondary 46E25, 20C20
Cite as: arXiv:2204.08991 [physics.class-ph]
  (or arXiv:2204.08991v2 [physics.class-ph] for this version)
  https://doi.org/10.48550/arXiv.2204.08991

Submission history

From: Evelyn Sander [view email]
[v1] Mon, 18 Apr 2022 14:30:26 UTC (28,514 KB)
[v2] Thu, 27 Oct 2022 18:29:47 UTC (33,286 KB)
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