Hamilton equations for elasticae in the Euclidean 3-space.
| dc.contributor.author | Pozo Coronado, Luis Miguel | |
| dc.date.accessioned | 2023-06-20T17:06:02Z | |
| dc.date.available | 2023-06-20T17:06:02Z | |
| dc.date.issued | 2000 | |
| dc.description.abstract | The variational problem on spatial curves defined by the integral of the squared curvature, whose solutions are the elasticae or nonlinear splines, is analyzed from the Hamiltonian point of view, using a procedure developed by Munoz Masqueand Pozo Coronado [J. Munoz Masque, LM. Pozo Coronado, J. Phys. A 31 (1998) 6225-6242]. The symmetry of the problem under rigid motions is then used to reduce the Euler-Lagrange equations to a first-order dynamical system. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGESIC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17489 | |
| dc.identifier.doi | 10.1016/S0167-2789(00)00040-3 | |
| dc.identifier.issn | 0167-2789 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/journal/01672789 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57769 | |
| dc.issue.number | 3-4 | |
| dc.journal.title | Physica D | |
| dc.language.iso | eng | |
| dc.page.final | 260 | |
| dc.page.initial | 248 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PB98-0533. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Hamilton equations | |
| dc.subject.keyword | Elasticae | |
| dc.subject.keyword | Generalized symmetries | |
| dc.subject.keyword | variational problem | |
| dc.subject.keyword | Spatial curves | |
| dc.subject.keyword | squared curvature | |
| dc.subject.keyword | Rigid body motions | |
| dc.subject.keyword | Euler-Lagrange equations | |
| dc.subject.keyword | Firstorder dynamical system | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Hamilton equations for elasticae in the Euclidean 3-space. | |
| dc.type | journal article | |
| dc.volume.number | 141 | |
| dcterms.references | R. Abraham, J.E. Marsden, Foundations of Mechanics, 2nd Edition, Benjamin/Cummings, Menlo Park, CA, 1978. V.I. Arnold, Mathematical Methods of Classical Mechanics,2nd Edition, Springer, Berlin, 1989. G. Brunnett, P.E. Crouch, Elastic curves on the sphere,Adv. Comput. Math. 2 (1994) 23–40. R. Bryant, P. Griffiths, Reduction for constrained variational problems and the integral of the squared curvature, Am. J. Math. 108 (1986)525–570. G.C. Constantelos, On the Hamilton–Jacobi theory with derivatives of higher order, Nuovo Cimento B 84 (1984)91–10. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1970. K. Foltinek, The Hamiltonian theory of elastica, Am. J.Math. 116 (1994) 1479–1488. M. Giaquinta, S. Hildebrandt, Calculus of Variations II:The Hamiltonian Formalism, Springer, Berlin, 1996. H. Goldschmidt, S. Sternberg, The Hamilton–Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble) 23 (1) (1973)203–267. P.A. Griffiths, Exterior Differential Systems and the Calculus of Variations, Birkhaüser, Boston, MA, 1983. H.W. Guggenheimer, Differential Geometry, McGraw-Hill, New York, 1963. S. Kehrbaum, J.H. Maddocks, Elastic rods, rigid bodies,quaternions and the last quadrature, Philos. Trans.Roy. Soc. London Ser. A 355 (1997) 2117–2136. N. Koiso, Elasticae in a Riemannian manifold, Osaka J.Math. 29 (1992) 539–543. J. Langer, D.A. Singer, The total squared curvature of closed curves, J. Differential Geom. 20 (1984) 1–22. J. Langer, D.A. Singer, Hamiltonian aspects of the Kirchhoff elastic rod, Preprint, 1992. J. Langer, D.A. Singer, Lagrangian aspects of the Kirchhoff elastic rod, SIAM Rev. 38 (1996) 605–618. A. Linnér, Existence of free nonclosed Euler–Bernoulli elastica, Nonlinear Anal. 21 (1993) 575–593. J.D. Logan, Invariant Variational Principles, Academic Press, New York, 1977. L. Lusanna, The second Noether theorem as the basis of the theory of singular Lagrangian and Hamiltonian constraints, Riv. Nuovo Cimento 14 (1991) 1–75. J. Muñoz Masqué, Formes de structure et transformations infinitésimales de contact d’ordre supérieur, C.R. Acad. Sci. Paris Sé. I 298 (1984) 185–188. J. Muñoz Masqué, Poincaré–Cartan forms in higher order variational calculus on fibred manifolds,Rev.Mat.Iberoamericana 1 (1985)85–126. J. Muñoz Masqué, L.M. Pozo Coronado, Parameter-invariant second-order variational problems in one variable, J. Phys. A 31 (1998)6225–6242. P.J. Olver, Equivalence, Invariants, and Symmetry,Cambridge University Press, Cambridge, 1995. R.S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Am. Math. Soc. 22 (1957) 1–123. J.M. Pons, Ostrogradski’s theorem for higher-order singular Lagrangians, Lett. Math. Phys. 17 (1989) 181–189. S. Sternberg, Some preliminary remarks on the formal variational calculus of Gel’fand and Dikii, Lecture Notes in Math. 676 (1978)399–407. D.J. Struik, Lectures on Classical Differential Geometry, 2nd Edition, Addison-Wesley, Reading, MA, 1961. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0124d449-632e-4dc8-9651-eb1975f330ab | |
| relation.isAuthorOfPublication.latestForDiscovery | 0124d449-632e-4dc8-9651-eb1975f330ab |
Download
Original bundle
1 - 1 of 1