2. The wave height is small so that all wave and body motions 

 can be linearized. 



3. The body is a rigid slender body of revolution. 



4. The mooring cable is inelastic; its dynamics can be 

 neglected, and it is attached to the body through a friction- 

 less joint below the body axis. 



5. The body is ballasted to lie in the horizontal plane. 



6. The fluid is deep. 



We utilize two Cartesian coordinate systems, (x, y, z) and (5, n, 



?) , with (x, y, z] fixed in space and (5, n, C) fixed in the body (Figure 



1) . The C-axis is the body axis, and when the body is in equilibrium 



this coincides with the horizontal x-axis. The z-axis is chosen to be 



vertical and positive upwards. The body is fastened to the mooring cable 



at the point (0, 0, -I), where £ is the length of the arm. The centers 



of buoyancy and gravity of the body are assumed to lie at (?pr>, 0, 0) and 



(C , 0, C„^) , respectively. (Note that ^ = is a result of neglecting 

 CG CG Ct) 



the small buoyancy of the arm.) Since the body is ballasted to rest in 

 the horizontal position, it follows that 



M 5cG = P ^ ?CB [1^ 



where M is the body mass; p is the fluid density; and Y is the body volume. 

 The tension in the mooring cable is 



T = pg V - Mg [2] 



where g is the gravitational constant. 



Restricting ourselves to analysis of motions in the vertical plane, 

 these will consist of a surge displacement C , heave displacement c, , . and 

 pitch displacement 0. However, the restraint of the mooring cable (with 

 the origin directly above the mooring- attachment point) will restrain ,the 

 heave displacement to a second-order amplitude, which may be neglected in 

 linearized analysis. As a consequence of the surge and pitch displace- 

 ments £ and 9, the two coordinate systems may be related as follows: 

 o 



x-C =Ccose+c sin 6 = 5 + ^6 [3] 



