Control of Fields

Abstract

The theoretical representation of classical mechanics and field theory is very similar in some ways. This also applies to the axiomatic structure. It is well known that essential aspects of the classical mechanics can be translated into the language of field theory. Especially, there exist equivalent relations between the canonical formalism of the field theory and of the classical mechanics with respect to the Hamilton principle and the Euler–Lagrange equations. Let us briefly study the basic ideas of the variational principle for classical fields, in particular, with respect to some specific features occurring in field theoretical equations. This is not the place to discuss the mathematical and physical details of this well–established theoretical concept. The interested reader may find more information in the literature [1–4]. But this very short overview should give at least a guideline for the following chapter, namely for the translation of the previously demonstrated variational method for the control of systems with a finite set of degrees of freedom to the variational method for the control of fields.