Brard 
Casec - a = 0; the motion of the body consists ofa 
translation nearly uniform with small variations 
of V,,(0) and o, 
In that case, the support of the free vortex sheet x f is 
practically the same as in case b. This case will be studied in some 
details in the next Section. 
VII - HYDRODYNAMIC FORCES EXERTED ON THE BODY 
The case a previously defined (Section VI) can be subdivided 
into two cases, a, , a, according as the motion of the body is uni- 
form or not. 
Case a7 The body is in uniform motion 
Since Vie is nullinside D, and no free vortex is shed by 
the body, the fluid,motion is steady with respect to the system of 
axes S. Hence C*R =0 inside D,, and in this domain, Euler's 
equation ot 
dV 
SN anal = 
p ais dt 
reduces to 
l ae 1 2 
— V Se a ee -V (— 
Pn ashe Vag Be Ca AR 
1 2 a 1 Z 
- V(— Q - = i i 
(3 me? 5 Vp) inside D, 
We have therefore 
tak. i _lbsietsn uF bay? 
? P4(M.) =F aS (M.) a VRiM,) + constant on 2d. CH. 1) 
The system oA of hydrodynamic forces exerted on the body consists 
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