Computing Hearing and Pitching Motions 485 
The formula for the boundary of the contour is expressed in nondimensional form as 
follows: 
(riz =) 6 ales 2° oF tbteg 2", (1) 
The following formulae for the potential and for the stream function caused by a heaving 
motion are applied: 
foo) 
Kz 
=U [A, Lim | £8082 BY) wag 
10 Koy te Stl 
ie) fo) 
n-1 
+ Pa A. | Ke J (K+v) e*? cos (Ky) ck 
n=1 0 
(2) 
oo) . 
enue a im or Shisarie (Ks) 
¥ | ep ” K-~v+ ip 
© (0) 
2(n-1) em ee 
+ A, K (K+v) e*? sin (Ky) cK 
n=1 0 
The time factor e’®* has been omitted. U describes the amplitude of the oscillatory ve- 
locity of the body. Both the condition of continuity and the condition on the free surface 
are satisfied. The problem is now to define the coefficients a such that the condition on 
the boundary of the contour is also satisfied. This requires a sufficient number of terms in 
the rows to be considered. 
The condition on the boundary of the contour for the heaving motion is 
we Uy: (3) 
In case (b) — the restrained body in transverse waves — a surface wave with the orbital 
velocity 1 is assumed so that 
