Principle of Minimum Potential Energy
Purpose of Lesson To introduce the principle of minimum potential energy and the concept of a functional (a function of a function).
The equations of statics that govern the behavior of discrete systems result when the potential energy function is minimized using the procedures of differential calculus. When the principle is extended to continuous systems, the potential energy function that must be minimized is found to be a functional. The emergence of the need to minimize a functional provides the motivation for Lesson 2, which introduces the calculus of variations, the branch of mathematics used to identify the conditions required to minimize the potential energy functional.
The principle of ...
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