Dissertation
Bicycle geodesics in the plane, the sphere, and the hyperboloid
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2024
DOI:
https://doi.org/10.17918/00010459
Abstract
There has been a growing interest in the kinematics of bicycle motion. A line segment subject to a bicycle motion is constrained by the no-slip condition, a nonholonomic constraint where the velocity of the rear point is in the direction of the bicycle frame, the line segment connecting the front and the rear point. We want to find the minimal path of the front wheel of the bicycle from one position to another. This problem can be interpreted as a variational problem and we can define and construct a Hamiltonian system of differential equations. The solution path turns out to be an elastica. We will also analyze a third point called the 'traintrack' which exhibits very interesting properties including both the front and the traintrack having an arc-length parametrized curve. We first analyze bicycle motion of a line segment in the plane and then extend these results to bicycle geodesics in the sphere and the hyperboloid.
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Details
- Title
- Bicycle geodesics in the plane, the sphere, and the hyperboloid
- Creators
- Wonsang Cho
- Contributors
- Ronald K. Perline (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- 40 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991021890112504721