High-Order Splines on Riemannian Manifolds

Margarida Camarinha ; Fátima Silva Leite ; Peter E. Crouch

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 172-193.

Résumé

This paper is an overview of the work of the authors about generalized polynomial curves and splines on Riemannian manifolds. The emphasis is put on the variational approach that gives rise to such curves, and on the Hamiltonian formulation for the cubic case.

Détail

Keywords: Riemannian polynomial splines, variational problems, generalized Jacobi fields and conjugate points, $m$-exponential, optimal control, Hamiltonian equations.
Mots-clés : Euler–Lagrange equations

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