Volume 25, 2019
|Number of page(s)||38|
|Published online||05 July 2019|
Swim-like motion of bodies immersed in an ideal fluid
Dip. di Matematica, Università di Padova,
via Trieste 63,
* Corresponding author: firstname.lastname@example.org
Accepted: 18 March 2017
The connection between swimming and control theory is attracting increasing attention in the recent literature. Starting from an idea of Alberto Bressan [A. Bressan, Discrete Contin. Dyn. Syst. 20 (2008) 1–35]. we study the system of a planar body whose position and shape are described by a finite number of parameters, and is immersed in a 2-dimensional ideal and incompressible fluid in terms of gauge field on the space of shapes. We focus on a class of deformations measure preserving which are diffeomeorphisms whose existence is ensured by the Riemann Mapping Theorem. After making the first order expansion for small deformations, we face a crucial problem: the presence of possible non vanishing initial impulse. If the body starts with zero initial impulse we recover the results present in literature (Marsden, Munnier and oths). If instead the body starts with an initial impulse different from zero, the swimmer can self-propel in almost any direction if it can undergo shape changes without any bound on their velocity. This interesting observation, together with the analysis of the controllability of this system, seems innovative.
Mathematics Subject Classification: 74F10 / 74L15 / 76B99 / 76Z10
Key words: Swimming / Ideal fluid / Control / Gauge theory
© EDP Sciences, SMAI 2019
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