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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 172–193
DOI: https://doi.org/10.4213/tm4324 (Mi tm4324) 		 
This article is cited in 4 scientific papers (total in 4 papers)

High-Order Splines on Riemannian Manifolds

Margarida Camarinhaa, Fátima Silva Leitebc, Peter E. Crouchd

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
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DOI: https://doi.org/10.4213/tm4324
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.
Funding agency Grant number
Fundação para a Ciência e a Tecnologia UIDB/00324/2020
UIDP/00048/2020
The work of Margarida Camarinha was partially supported by the Centre for Mathematics of the University of Coimbra, project UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. Fátima Silva Leite acknowledges Fundação para a Ciência e Tecnologia (FCT-Portugal) and COMPETE 2020 program for the financial support to the project UIDP/00048/2020.
Received: March 17, 2022
Revised: July 23, 2022
Accepted: February 23, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 158–178
DOI: https://doi.org/10.1134/S0081543823020128
Bibliographic databases:
Document Type: Article
UDC: 514.764+517.977
Language: Russian
Citation: Margarida Camarinha, Fátima Silva Leite, Peter E. Crouch, “High-Order Splines on Riemannian Manifolds”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 172–193; Proc. Steklov Inst. Math., 321 (2023), 158–178
Citation in format AMSBIB
\Bibitem{CamSilCro23}
\by Margarida~Camarinha, F\'atima~Silva~Leite, Peter~E.~Crouch
\paper High-Order Splines on Riemannian Manifolds
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 172--193
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4324}
\crossref{https://doi.org/10.4213/tm4324}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 158--178
\crossref{https://doi.org/10.1134/S0081543823020128}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85170845175}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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