Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)

Alexey Mashtakov, Andrei Ardentov, Yuri Sachkov

In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that t…