  The purpose of this paper is to revisit the infinite Lie group theoretical
framework of hydrodynamics developped by V. Arnold in 1966. First of all, we
extend this approach from the Lie pseudogroup of volume preserving
transformations to an arbitrary Lie pseudogroup. Then we prove that, contrary
to what could be believed from the work of Arnold which is of a purely
analytical nature, the same results can be obtained from a purely formal point
of view. Finally, we provide the analogue for both the so-called "body" and
"space" dynamical equations. We conclude by showing that even this new approach
can be superseded by dynamics on Lie groupoids, along ideas pioneered by the
brothers E. and F. Cosserat or H. Weyl at the beginning of the last century, on
the condition to change the underlying philosophy.
