  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).
