Bicycling geodesics and elasticae
Title: Bicycling geodesics and elasticae
Starts: 12:00 on Wednesday January 17, 2024
Ends: 13:30 on Wednesday January 17, 2024
Location: Virtual
Speaker: Sergei Tabachnikov
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Institution: Pennsylvania State University
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Abstract:
One models a bicycle as a directed segment of a fixed length that can move so that the velocity of the rear end is always aligned with the segment. A bicycle path is a motion of the segment, and the length of the path, by definition, is the length of the front track. This defines a problem of sub-Riemannian geometry, and one wants to describe the respective geodesics. The first such problem, concerning planar bicycle motion, was the subject of R. Montgomery’s talk at this seminar about two years ago. I shall recall these results, and present two variations on this theme: the bicycle motion in multidimensional Euclidean space, and the planar motion of a 2-linkage (a tricycle?). A number of open problems will be formulated.
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