Rolling Geodesics, Mechanical Systems and Elastic Curves

This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem. We show remarkable connections between these two problems manifested by the associated Hamiltonians obtained by the Maximum Principle of optimal control. We also show that each of these Hamiltonians is completely intergrable, in the sense of Liouville. Finally we demonstrate the significance of these results for the theory of mechanical systems.

Automated summary

This paper defines a class of differentiable manifolds that include two distinct optimal problems - affine-quadratic and rolling problem, and shows remarkable connections between these problems through the associated Hamiltonians obtained by optimal control. It also demonstrates that each of these Hamiltonians is completely integrable in the sense of Liouville. Finally, the significance of these results for the theory of mechanical systems is demonstrated.