A new formulation for the inverse problem of the variations calculus

Abstract

The variational calculus is directly related to the energetic modeling of physical systems in general. The advantage of such approach in relation to the classical approaches (Newtonians) is that a system can be subdivided in many sub-systems whose modeling can be simpler than the one of the whole. As the total energy of a system is the sum of the energy of the parts, it is possible to obtain a global result from the partial results. Nevertheless, in the classic methods, based on force, such flexibility does not exist, the most possible way is to apply the effect superposition method. However, this method does not apply to non-linear systems. In general, the engineering applications are always linked to the solution of a set of descriptive equations of the phenomena. Starting in these equations and reaching a functional, which represent them, is the inverse problem of the variational calculus. This paper presents a new method for reach a variational formulation of non-potent operators is introduced. A variational formulation to complete Navier-Stokes equations has been developed.