Skateboard Tricks and Topological Flips

• Published in 2021
• Added on 2021-08-29

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.

Links

• http://arxiv.org/abs/2108.06307v1
• http://arxiv.org/pdf/2108.06307v1

Other information

BibTeX entry

@article{SkateboardTricksandTopologicalFlips,
	key = {SkateboardTricksandTopologicalFlips},
	type = {article},
	title = {Skateboard Tricks and Topological Flips},
	author = {Justus Carlisle and Kyle Hammer and Robert Hingtgen and Gabriel Martins},
	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.},
	comment = {},
	date_added = {2021-08-29},
	date_published = {2021-10-09},
	urls = {http://arxiv.org/abs/2108.06307v1,http://arxiv.org/pdf/2108.06307v1},
	collections = {attention-grabbing-titles,easily-explained,games-to-play-with-friends,geometry,the-groups-group},
	url = {http://arxiv.org/abs/2108.06307v1 http://arxiv.org/pdf/2108.06307v1},
	year = 2021,
	urldate = {2021-08-29},
	archivePrefix = {arXiv},
	eprint = {2108.06307},
	primaryClass = {math-ph}
}