Publication: Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space
Loading...
Full text at PDC
Publication Date
2000
Authors
Muñoz Masqué, Jaime
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Natsional. Akad. Nauk Ukraïni, Inst. Mat., Kiev,
Citations
Exportar
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.
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
UCM subjects
Unesco subjects
Keywords
Citation
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.