Margarida Camarinha, Fátima Silva Leite, Peter E. Crouch, “High-Order Splines on Riemannian Manifolds”, Trudy Mat. Inst. Steklova, 2023, Volume 321,Pages <nobr>172

This article is cited in 4 papers

High-Order Splines on Riemannian Manifolds

Margarida Camarinha^a, Fátima Silva Leite^bc, Peter E. Crouch^d

^a CMUC, University of Coimbra, Department of Mathematics, 3000-143 Coimbra, Portugal
^b Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal
^c Institute of Systems and Robotics, UC, 3030-290 Coimbra, Portugal
^d College of Engineering, University of Texas at Arlington, Arlington, TX 76019-0019, USA

Abstract: 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.

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

UDC: 514.764+517.977

Received: March 17, 2022
Revised: July 23, 2022
Accepted: February 23, 2023

DOI: 10.4213/tm4324