Euler-Lagrange equations

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If they can be calculated, the trivial first integrals are also returned.

The first integrals are set equal to generated global indexed variables Ki that denote arbitrary constants.

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For higher-order functionals, for example, f(t, y(t), y'(t), y''(t)), use variables to represent derivatives. For example, set x1(t) = y(t) and x2(t)=y'(t), and then determine the Euler-Lagrange equations of the functional f + L*( x1'(t) - x2(t) )^2. To find the equations for the higher-order problem, substitute x2(t) = x1'(t) into the result.

Have a look at https://www.maplesoft.com/support/help/category.aspx?cid=449

You may get more help if you provide more information about the problem you hope to solve.

Dear doctor

Go To

Hillyard, Cinnamon, "A Maple Package for the Variational Calculus" (1992). All Graduate Theses and Dissertations. 7124. https://digitalcommons.usu.edu/etd/7124

DOI

https://doi.org/10.26076/2aaf-a411

"Abstract

The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete listing of the Maple code for HELMHOLTZ is found in an appendix."