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Symmetries and order reduction for elasticae in surfaces of constant curvature.

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Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel (1999) Symmetries and order reduction for elasticae in surfaces of constant curvature. In Group 22: Proceedings of the 12th International Colloquium on Group Theoretical Methods in Physics. International Press, Cambridge, pp. 320-324. ISBN 9781571460547



Abstract

Parameter invariance of the variational problem associated to the squared curvature Lagrangian, whose extremals are the elasticae, allows us to find an equivalent,nonparametric variational problem which is regular. Hamiltonian formalism is then applied to the new Lagrangian, and the order of the resulting Hamilton equations is reduced by using the invariance under isometries of the problem. For a constant curvature
surface the number of isometries allows us to perform this reduction to obtain a planar nonlinear ordinary differential equation of the first order.


Item Type:Book Section
Uncontrolled Keywords:Surfaces of constant curvature; Variational problem; Squared curvature Lagrangian; Elasticae; Hamiltonian formalism; Invariance under isometries
Subjects:Sciences > Mathematics > Geometry
ID Code:21731
Deposited On:07 Jun 2013 14:05
Last Modified:12 Dec 2018 15:13

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