Skateboard Tricks and Topological Flips

TL;DR

This paper models skateboard flip tricks as curves in the rotation group SO(3), classifies them into four types, and provides explicit formulas for their deformations, offering a topological perspective on skateboarding maneuvers.

Contribution

It introduces a topological framework for classifying flip tricks as curves in SO(3) and derives explicit deformation formulas, a novel approach in skateboarding motion analysis.

Findings

Only four flip tricks exist up to continuous deformation.

Explicit formulas for tricks and their deformations are derived.

The analysis uses liftings to the unit 3-sphere.

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.