Elements of the Calculus of Variations
Purpose of Lesson To introduce the concepts or elements of the calculus of variations and use them to develop the necessary conditions for minimizing functionals.
The principles of variational calculus are used here to identify the conditions that must hold if a functional is to be minimized. We show that minimization is accomplished when the Euler-Lagrange equations and the boundary terms are forced to zero. The process of satisfying these conditions produces the governing differential equations and boundary conditions for a problem. In the case of the elasticity problems studied, the resulting governing differential equations are equilibrium equations.
The developments of this lesson define the ...
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