Chapter X

Calculus of Variations

Keywords

Action integral; Stationary functional depending on a single function; Generalised Cartan form; Euler-Lagrange form; Euler-Lagrange equations; Adjoint equations; Energy-momentum tensor; Noetherian vector fields; First and second kind Noetherian vector fields; Conservation laws; Variational symmetries; Action integral depending on several functions; Euler-Lagrange equations for the general case

10.1 Scope of the Chapter

This chapter is devoted to a brief study of the calculus of variations that deals with determining functions rendering a functional defined as an integral over a function space stationary. However, in contrast to the classical approach, we will be employing exterior analysis throughout the ...

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