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Mathematical Physics

arXiv:2108.06307 (math-ph)
[Submitted on 13 Aug 2021]

Title:Skateboard Tricks and Topological Flips

Authors:Justus Carlisle, Kyle Hammer, Robert Hingtgen, Gabriel
Martins
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    Abstract: We study the motion of skateboard flip tricks by
    modeling them as continuous curves in the group $SO(3)$ of
    special orthogonal matrices. We show that up to continuous
    deformation there are only four flip tricks. The proof relies on
    an analysis of the lift of such curves to the unit 3-sphere. We
    also derive explicit formulas for a number of tricks and
    continuous deformations between them.

Comments:   20 pages, 12 figures
Subjects:   Mathematical Physics (math-ph); Differential Geometry
            (math.DG)
MSC         53Z05 (Primary), 22C05, 70E15 (Secondary)
classes:
Cite as:    arXiv:2108.06307 [math-ph]
            (or arXiv:2108.06307v1 [math-ph] for this version)

Submission history

From: Gabriel Martins [view email]
[v1] Fri, 13 Aug 2021 16:28:59 UTC (1,859 KB)
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