Exploring the 3D Analog of the Proof of the 2D Isostatic Theorem for Sticky Disks
Citation
Macha, Venkata V. 2019. Exploring the 3D Analog of the Proof of the 2D Isostatic Theorem for Sticky Disks. Bachelor's thesis, Harvard College.Abstract
The 2D Isostatic Theorem reveals that a packing of n disks with generic radii can have at most 2n − 3 disk pairs in contact. The motive of this thesis is to analyze the 3D analog of the 2D Isostatic Theorem proof and determine the truth of its dependencies within R^3. Through theoretical and computational methods, we have discovered that in R^3, Sg isn’t necessarily a smooth sub-manifold of dimension 4n − m (disproving the first dependency) and that (G, p) can have nontrivial edge-length stress equilibrium vectors (disproving the second dependency). Finally, in our search through the Miranda dataset of all possible packings where n ≤ 14, we determined that there were no additional examples where edge-length stress equilibrium vectors exist.Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAACitable link to this page
https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37364600
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