Rolling Geodesics, Mechanical Systems and Elastic Curves

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

Mathematics, 2022, vol. 10, issue 24, 1-24

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.

Keywords: Lie groups; Lie algebras; homogeneous manifolds; Hamiltonians; Poisson bracket; mechanical tops (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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