Abstract
In this chapter Euler-Lagrange equations and the boundary conditions for a given Functional with only one independent variable with second order derivatives are derived. A general approach for solving one dimensional structures follows next. Euler-Lagrange equation leading to optimization is explained next by considering Brachistochrone problem. The derivation of Euler-Lagrange equation and boundary conditions is also presented by using an operator denoted as delta (δ).
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Rao, J.S. (2017). Euler-Lagrange Equations. In: Simulation Based Engineering in Solid Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-319-47614-8_3
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DOI: https://doi.org/10.1007/978-3-319-47614-8_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47613-1
Online ISBN: 978-3-319-47614-8
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