Sergei Tabachnikov (The Pennsylvania State University)

Title:
Elastica, filament equation, and bicycle models

Abstract:

Elastica are solutions to a classic variational problem of Bernoulli: to describe the curves of fixed lengths that extremize the bending energy. I will describe several problems where these ubiquitous curves appear.

One is the study of the filament equation, a completely integrable evolution on curves that models the propagation of vortices in liquid or gas. Another is a simple model of a bicycle, presented 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, subject to this nonholonomic constraint, and the length of the path, by definition, is the length of the front track. This defines a problem of sub-Riemannian geometry, and  the respective geodesics are closely related to classical elastica and its "relatives". Another bicycle problem where elastica appears is as follows: given the front and rear bicycle tracks, can one determine which way the bicycle went?

Schedule:

10:00 - 11:30 RTG Lecture 1 (Manuel Krannich) | 5. OG, Konferenzraum

11:30 - 12:00 Get-Together with speaker | 5. OG, Common Room

12:00 - 13:00 Common lunch | reserved at BräuStadel

13:00 - 13:30 Informal meeting of PhD students | 5. OG, Common Room

13:30 -14:30 RTG colloquium: Sergei Tabachnikov | EG, Seminarraum C

14:30 - 15:15 Common tea | 5. OG, Common Room

15:15 - 16:45 RTG Lecture 2 (Manuel Krannich) | 5. OG, Konferenzraum

HD