Swim-like motion of bodies immersed in an ideal fluid

TL;DR

This paper explores how bodies immersed in an ideal fluid can achieve self-propulsion through shape changes, extending previous work to cases with initial impulse and analyzing controllability in a fluid-structure interaction context.

Contribution

It introduces a novel analysis of self-propulsion with initial impulse in ideal fluids and investigates controllability of shape-changing bodies in this setting.

Findings

Bodies with initial impulse can self-propel in almost any direction.

Shape changes without velocity bounds enable propulsion regardless of initial conditions.

The controllability of the system is analyzed and found to be feasible under certain conditions.

Abstract

The connection between swimming and control theory is attracting increasing attention 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 described by a finite number of parameters, and is immersed in a 2-dimensional ideal and in-compressible 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. We face a crucial problem: the pres-ence 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.