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Rolling Geodesics, Mechanical Systems and Elastic Curves

Author

Listed:
  • Velimir Jurdjevic

    (Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3, Canada)

Abstract

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.

Suggested Citation

  • Velimir Jurdjevic, 2022. "Rolling Geodesics, Mechanical Systems and Elastic Curves," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4827-:d:1007757
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    Citations

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    Cited by:

    1. Alexey Mashtakov & Yuri Sachkov, 2023. "Time-Optimal Problem in the Roto-Translation Group with Admissible Control in a Circular Sector," Mathematics, MDPI, vol. 11(18), pages 1-31, September.
    2. Velimir Jurdjevic, 2023. "Integrable Systems: In the Footprints of the Greats," Mathematics, MDPI, vol. 11(4), pages 1-44, February.

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