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Variational problems on Lie groups and their homogeneous spaces: Elastic curves, tops, and constrained geodesic problems. (English) Zbl 1142.49317
Anzaldo-Meneses, A. (ed.) et al., Contemporary trends in nonlinear geometric control theory and its applications. International conference, México City, México, summer 2000. Dedicated to Velimir Jurdjevic on his 60th birthday. Singapore: World Scientific (ISBN 981-02-4841-5). 3-51 (2002).
From the text: The authors study a class of variational problems with quadratic cost. They paper expose the various connections between optimal control, variational problems, and Hamiltonian systems for systems on the isometry groups of \(\mathbb R^n\), \(\mathbb S^n\), and \(\mathbb H^n\), including the elastica problem first studied by Euler, and the ones of Delaunay and Dubins.
For the entire collection see [Zbl 0984.00078].

49K27 Optimality conditions for problems in abstract spaces
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
49N10 Linear-quadratic optimal control problems
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)