Vol. 9, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
Polygonal bicycle paths and the Darboux transformation

Ian Alevy and Emmanuel Tsukerman

Vol. 9 (2016), No. 1, 57–66
Abstract

A bicycle (n,k)-gon is an equilateral n-gon whose k diagonals are of equal length. In this paper we introduce periodic bicycle (n,k)-paths, which are a natural variation in which the polygon is replaced with a periodic polygonal path, and study their rigidity and integrals of motion.

Keywords
bicycle polygons, tire track problem, floating bodies in equilibrium
Mathematical Subject Classification 2010
Primary: 37J35, 52C25
Milestones
Received: 7 September 2013
Revised: 1 September 2014
Accepted: 8 December 2014
Published: 17 December 2015

Communicated by Kenneth S. Berenhaut
Authors
Ian Alevy
Division of Applied Mathematics
Brown University
Providence, RI 02912
United States
Emmanuel Tsukerman
Department of Mathematics
University of California, Berkeley
Berkeley, CA 94720
United States