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Using Cartan's exterior calculus, we derive a coordinate-free formulation ofthe Euler equations. These equations are invariant under Galileiantransformations, which constitute a global symmetry. With the introduction ofan appropriate generalized Coriolis force, these equations become symmetricunder general coordinate transformations.  We show how exterior calculus simplifies dramatically the derivation ofconservation laws. We also discuss the advantage of an exterior calculusformulation with respect to symmetry-preserving discretizations of theequations.

Fluid dynamics in the spirit of Cartan: A coordinate-free formulation of fluid dynamics for an inviscid fluid in inertial and non-inertial frames