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Given a principal bundle G \rightarrow P \rightarrow B (each being compact,connected and oriented) and a G-invariant metric h^{P} on P which induces avolume form \mu^{P}, we consider the group of all unimodular automorphismsSAut(P,\mu^{P}):={\varphi\in Diff(P) | \varphi^{*}\mu^{P}=\mu^{P} and \varphiis G-equivariant} of P and determines its Euler equation a la Arnold. Theresulting equations turn out to be (a particular case of) the Euler-Yang-Millsequations of an incompressible classical charged ideal fluid moving on B. It isalso shown that the group SAut(P,\mu^{P} is an extension of a certain volumepreserving diffeomorphisms group of B by the gauge group Gau(P) of P.

The group of unimodular automorphisms of a principal bundle and the Euler-Yang-Mills equations