Conference abstracts

Session B3 - Symbolic Analysis

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Discrete Moving Frames and Noether’s Finite Difference Conservation Laws. Euler’s Elastica.

Ana Rojo-Echeburúa

University of Kent, United Kingdom   -

Discrete moving frames have the potential to have a large spectrum of applications as well as leading to improvement regarding computations. Further, the theory of discrete moving frames provides an useful tool when solving variational problems or in the study of integrable systems. In this poster I will consider the discrete variational problem analogue to the minimisation of the integral of the curvature squared. The solutions of this equation are commonly known as Euler’s elastica. I will show that the Euler-Lagrange difference equations and the Noether’s difference conservation laws can be written in terms of the invariants of the action and a discrete moving frame and that the appearance of the moving frame in the expression for the conservation laws makes explicit the equivariance of the frame under the group action. I will exhibit how this formulation can allow one, to solve for the solutions in term of the original variables. By matching the use of the smooth and discrete frames, for the smooth and discrete problems respectively, I will show that it is possible to design approximations which have matching conservation laws.

Joint work with Elizabeth Mansfield (University of Kent, UK).

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FoCM 2017, based on a nodethirtythree design.