Systems and Lagrangian systems

Abstract

This chapter is devoted to a tentative classification of Lagrangian systems of conservation laws. Such a definition is of course far from unique. For instance, one might state that a Lagrangian system comes from continuum mechanics and is written in Lagrangian variables. This possible definition, which in some sense corresponds to the material presented in chapter 1 is not the one employed in the present chapter. Instead we will rely on the entropy of the system, since it is a natural notion in continuum mechanics and is also central in the mathematical theory of systems of conservation laws.

The science must be dogmatic, i.e. it must prove its conclusions strictly a priori from the secure principles.

– Immanuel Kant

(Critique of Pure Reason, 1781)