# Bicycle Rides

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Hundreds of millions of people ride bicycles every day. Yet only a small fraction are aware of the multitude of beautiful mathematics and physics involved. Describing a bicycle ride requires the mechanics of nonholonomic multi‐body systems, control theory, and algebraic geometry.

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Contributed by: Michael Trott with permission of Springer (March 2011)

From: *The Mathematica GuideBook for Numerics*, second edition by Michael Trott (© Springer, 2008).

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

For modeling bicycle rides in general, see:

D. J. N. Limebeer and R. S. Sharp, "Bicycles, Motorcycles and Models," *IEEE Control Systems Magazine*, 26(5), 2006 pp.34–61.

S. R. Dunbar, R. J. C. Bosman and S. E. M. Nooij, "The Track of a Bicycle Back Tire," *Mathematics Magazine*, 74(4), 2001 pp.273–287.

M. Levi and S. Tabachnikov. "On Bicycle Tire Tracks Geometry, Hatchet Planimeter, Menzin's Conjecture and Oscillation of Unicycle Tracks." (Feb 3, 2008) http://arxiv.org/pdf/0801.4396.

## Permanent Citation