Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space

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Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel (2000) Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space. In Proceedings of Institute of Mathematics of NAS of Ukraine. Proc. Inst. Math. Natl. Acad. Sci. Ukr.,, 1 (30). Natsional. Akad. Nauk Ukraïni, Inst. Mat., Kiev,, Ukrainian. Kyiv, pp. 170-176. ISBN 966-02-1401-4

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Official URL: http://www.slac.stanford.edu/econf/C990712/papers/art23.pdf



Abstract

The authors use the procedure developed in [9] to develop a Hamiltonian structure into the variational problem given by the integral of the squared curvature on the spatial curves.
The solutions of that problem are the elasticae or nonlinear splines. The symmetry of the problem under rigid motions is then used to reduce the Euler–Lagrange equations to a firstorder dynamical system.


Item Type:Book Section
Additional Information:

Proceedings of the third international conference on symmetry in nonlinear mathematical physics, Kyiv, Ukraine, July 12-18, 1999. Part 1. Transl. from the Ukrainian. Kyiv:
Institute of Mathematics of NAS of Ukraine

Uncontrolled Keywords:Variational problem; Nonlinear spline; Hamiltonian formalism; Generalized symmetry; Reduction
Subjects:Sciences > Mathematics > Differential equations
ID Code:21729
Deposited On:07 Jun 2013 14:03
Last Modified:02 Sep 2020 10:13

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