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.
more »
« less
Invariant Measures for Integrable Spin Chains and an Integrable Discrete Nonlinear Schrödinger Equation
- Award ID(s):
- 1763074
- PAR ID:
- 10143015
- Date Published:
- Journal Name:
- SIAM Journal on Mathematical Analysis
- Volume:
- 52
- Issue:
- 1
- ISSN:
- 0036-1410
- Page Range / eLocation ID:
- 135 to 163
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
An official website of the United States government

