In the aforegoing sections, Part I of this book, we consider the simplest problem of the calculus of variations, so called because it is indeed the simplest of a class of functional extremization problems. We restrict the discussion to functionals of integral type whose integrands depend on a scalar-valued variable x(t) and its derivative ẋ(t). Furthermore, we consider fixed end points; that is, we prescribe the initial and terminal values of t and x(t). A number of generalizations are of interest and are introduced below; while not treated in Part I, many are in fact subsumed in the class of problems discussed in Part II.
KeywordsVariational Approach Extremization Problem Simple Problem Piecewise Linear Function Admissible Function
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