Almost Lie structures on an anchored Banach bundle

Under appropriate assumptions, we generalize the concept of linear almost Poisson structures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the “Hilbert snake” as exposed in Pelletier and Saffidine (2011) [9].