Classical and relativistic fluids as intermediate integrals of finite dimensional mechanical systems

Abstract

We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of solutions of a finite dimensional mechanical system (a second order differential equation) are simultaneously Euler's equations of fluids and conversely. This will be done both in the classical and relativistic context. A direct relationship will be established by means of the so-called time constraint (classical unsteady case, static or not) and the relativistic correction (for arbitrary pseudo-Riemannian metrics).

arXiv commentarXiv admin note: text overlap with arXiv:1206.1372, arXiv:0801.4151 by other authors; Fixed a typo in the title

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