Seminar announcement

[Emanuele Tuillier Illingworth]

Speaker: Marta Zoppello (University of Padova)

Date: Wednesday, 4 December, 2013 - 14:00

Room: SISSA - Santorio A - room 133

Title: Controllability and locomotion in ideal fluids

Abstract: The connection between swimming and control theory is 
attracting increasing attention in the recent literature. Starting from 
an idea of Alberto Bressan [2] we study the system of a body whose 
position and shape are described by a finite number of parameters, and 
is immersed in an ideal and incompressible fluid. First of all we show 
that thanks to the linearity of the Euler’s equations which govern the 
motion of the fluid, the system’s Lagrangian is the sum of the kinetic 
energy of the body and of the fluid. Then, exploiting geometrical tools 
in control theory, used also in [1], we analyze the properties of the 
kinetic energy metric of these kind of systems and the consequences on 
their controllability. In particular we prove that we end up with an 
affine control system in which the presence of the drift depends on 
initial data. Finally we study the conditions in which they are 
controllable at least locally.

References:
[1] F. Cardin, M. Favretti. HYPER-IMPULSIVE MOTION ON MANIFOLDS. 
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS, vol. 4, p. 1-21, 
1998.
[2] A. Bressan. IMPULSIVE CONTROL OF LAGRANGIAN SYSTEMS AND LOCOMOTION 
IN FLUIDS. Personal web page: 'http://www.math.psu.edu/bressan/', 2007.
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