Principle of Least Dissipation

Abstract

The variational principles of ideal fluid and elastic body are all based on ignoring the dissipation. If the dissipation is not negligible, the governing equations do not have a variational structure, they possess a quasi-variational structure (see Sect. 2.6). In the another extreme case, when the dissipation plays the key role while the inertia and the internal energy effects are negligible, the variational structure of the governing equations appears again, but this is the variational structure of the non-equilibrium processes. This chapter is concerned with the corresponding variational principles. As has been mentioned in Sect. 2.6, these variational principles, in contrast to the least action principle, reflect the special features of the models used rather than the laws of Nature.