Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space
| dc.book.title | Proceedings of Institute of Mathematics of NAS of Ukraine | |
| dc.contributor.author | Muñoz Masqué, Jaime | |
| dc.contributor.author | Pozo Coronado, Luis Miguel | |
| dc.date.accessioned | 2023-06-20T21:06:29Z | |
| dc.date.available | 2023-06-20T21:06:29Z | |
| dc.date.issued | 2000 | |
| dc.description | 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 | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21729 | |
| dc.identifier.isbn | 966-02-1401-4 | |
| dc.identifier.officialurl | http://www.slac.stanford.edu/econf/C990712/papers/art23.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/60704 | |
| dc.issue.number | 30 | |
| dc.language.iso | eng | |
| dc.page.final | 176 | |
| dc.page.initial | 170 | |
| dc.publication.place | Ukrainian. Kyiv | |
| dc.publisher | Natsional. Akad. Nauk Ukraïni, Inst. Mat., Kiev, | |
| dc.relation.ispartofseries | Proc. Inst. Math. Natl. Acad. Sci. Ukr., | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Variational problem | |
| dc.subject.keyword | Nonlinear spline | |
| dc.subject.keyword | Hamiltonian formalism | |
| dc.subject.keyword | Generalized symmetry | |
| dc.subject.keyword | Reduction | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space | |
| dc.type | book part | |
| dc.volume.number | 1 | |
| dcterms.references | Constantelos G.C., On the Hamilton–Jacobi theory with derivatives of higher order, Nuovo Cimento B,1984, V.84, 91–101. Giaquinta M. and Hildebrandt S., Calculus of Variations II: The Hamiltonian Formalism, Springer-Verlag,Berlin, 1996. Goldschmidt H. and Sternberg S., The Hamilton–Cartan formalism in the calculus of variations, Ann. Inst.Fourier (Grenoble), 1973, V.23, N 1, 203–267. Griffiths P.A., Exterior Differential Systems and the Calculus of Variations, Birk¨auser, Boston, 1983. Langer J. and Singer D.A., The total squared curvature of closed curves, J. Diff. Geom., 1984, V.20, 1–22. Logan J.D., Invariant Variational Principles, Academic Press, New York, 1977. Lusanna L., The second Noether theorem as the basis of the theory of singular Lagrangians and Hamiltonians constraints, Riv. Nuovo Cimento, 1991, V.14, 1–75. Muñoz Masque J., Formes de structure et transformations infinitesimales de contact d’ordre superieur, C.R.Acad. Sci. Paris, 1984, V.298, Serie I, 185–188. Muñoz Masque J. and Pozo Coronado L.M., Parameter-invariant second-order variational problems in one variable, J. Ph ys. A: Math . Gen., 1998, V.31, 6225–6242. Olver P.J., Equivalence, Invariants and Symmetry, Cambridge University Press, 1995. Sternberg S., Some preliminary remarks on the formal variational calculus of Gel’fand and Dikii, Lect. Notes in Math., 1978, V.676, 399–407. Struik D.J., Lectures on Classical Differential Geometry, 2nd. Edition, Addison-Wesley, Reading, Massachusetts,1961. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0124d449-632e-4dc8-9651-eb1975f330ab | |
| relation.isAuthorOfPublication.latestForDiscovery | 0124d449-632e-4dc8-9651-eb1975f330ab |
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