The Formalism of the Calculus of Variations
One of the most beautiful and widely spread paradigms of science and mathematics in particular is that of minimum principles. It is strongly related to the everyday principle of economy of means and to the research of optimal strategies to realize our goals. Therefore, it is not surprising that since the beginning minimum principles have been used to formulate laws of nature.We have already seen a few examples in Chapter 6 of [GM1] and in this volume.
KeywordsHamiltonian System Lagrange Equation Lagrangian Formalism Canonical Transformation Jacobi Equation
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