Brard 
This paper has been written to suscitate new re- 
searches in the field of the maneuverability and 
control of marine vehicles. 
INTRODUCTION 
Fhe vortex theory in incompressible, inviscid and homogene- 
ous fluids plays a role of importance in many chapters of Ship Hydro- 
dynamics. However it is not systematically applied to all the problems 
where it should be especially useful. This is the case of those relat- 
ed to maneuverability and control of bodies which behave as rather 
poor lifting surfaces because of their large displacement/length 
ratios. The research reported in the present paper has thus been un- 
dertaken with the purpose of determining how much help one can ex- 
pect from the theory when dealing with such bodies in any given steady 
or unsteady motion, 
Indeed the question was not to draw up a new vortex theory, 
but rather to extend known results relevant to fluid kinematics and 
dynamics and to increase their generality and effectiveness. 
The joined table of contents suffices to show the writer's 
line of thought. 
The startpoint is Poincaré's formula which permits to deter- 
mine the velocity in a closed domain when the vorticity inside that 
domain and the velocity on its boundary are known. This leads toa 
mathematical model where the hull surface is replaced by a fluid 
surface moving without alteration of its shape. There exists an in- 
finite class of vortex distributions kinematically equivalent to the 
body. They only depend on the choice of the vorticity distribution in- 
side the hull. The most interesting one is that which permits the ex- 
terior fluid to be adherent to the hull. Inside the hull the absolute 
fictitious fluid motion coincides with that of the body. From the point 
of view of kinematics, one of the features of the theory is that the 
total vortex distribution can be divided into two families almost inde- 
pendent of each other. One consists of a volume distribution inside 
the hull and of a vortex sheet over the hull, it is so calculated as to 
induce outside the body a velocity which is null everywhere. It only 
depends on the angular velocity of the body and can be determined 
once for all for any given hull. The second family is the union of a 
vortex sheet distributed over the hull and of the free vortices shed 
by the hull. It is determined by the condition that the fluid inside the 
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