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The connection between swimming and control theory is attracting increasingattention in the recent literature. Starting from an idea of Alberto Bressan[7] we study the system of a planar body whose position and shape are describedby a finite number of parameters, and is immersed in a 2-dimensional ideal andin-compressible fluid in terms of gauge field on the space of shapes. We focuson a class of deformations measure preserving which are diffeomeorphisms whoseexistence is ensured by the Riemann Mapping Theorem. We face a crucial problem:the pres-ence of possible non vanishing initial impulse. If the body startswith zero initial impulse we recover the results present in literature(Marsden, Munnier and oths). If instead the body starts with an initial impulsedifferent from zero, the swimmer can self-propel in almost any direction if itcan undergo shape changes without any bound on their velocity. This interestingobservation, together with the analysis of the controllability of this system,seems innovative.

Swim-like motion of bodies immersed in an ideal fluid