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Preprint
Geometry of Integrable Linkages
arXiv.org
25 Jul 2023
Abstract
In analogy with the well-known 2-linkage tractor-trailer problem, we define a
2-linkage problem in the plane with novel non-holonomic ``no-slip'' conditions.
Using constructs from sub-Riemannian geometry, we look for geodesics
corresponding to linkage motion with these constraints (``tricycle
kinematics''). The paths of the three vertices turn out to be critical points
for functionals which appear in the hierarchy of conserved quantities for the
planar filament equation, a well known completely integrable evolution equation
for planar curves. We show that the geodesic equations are completely
integrable, and present a second connection to the planar filament equation.
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Details
- Title
- Geometry of Integrable Linkages
- Creators
- Ron PerlineSergei Tabachnikov
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021880180204721