Work

Geometry of Integrable Linkages

Year: 2025

Type: article

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.

Source: Journal of Experimental Mathematics

DOI: 10.56994/jxm.001.001.005

Authors: Ron Perline, Sergei Tabachnikov

Institutions: Drexel University, Pennsylvania State University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, University of Pennsylvania, Pennsylvania State University

Award: Topics in Kinematics and Geometrical Optics: Tire Track Geometry and Billiard Models