DYNAMICS AND KINEMATICS OF SUBM.\RINE CABLE 1197 



(c) 



(d) ^''^ 



(e) 



(f) 

 (g) 



Here k and X are constants, defined and plotted in Section 3.6, which de- 

 pend only on a, the critical angle corresponding to V. Equations (96) 

 and (97) form a complete set of equations in the unknowns Xi , Xi , 

 Si , S2 , To , Ts , 8, and a. They can be reduced to a set which contain 

 only the unknowns a and Ts : 



^■M 1 „;. 



(Pi{a) sin a — 6^2(0-) sin q; — Al 1 + \ .. t sin a 1 = 0, (a) 



\ ^2(0-) / 



f. = i+'j^, (b) 



(98) 



where 



h = wh/EA, 

 t = Vt/h, 

 Ts = Ts/wh, 



and 



<Pi = sinh (J — a -\- (cosh o- — 1) tan - — (X — k). 



cosh (T — 1 , . , 



<P2 = • 7 ■ + X + 0", 



tan a 

 cosh a- — 1 , . , 



(pZ — : + Sinh (T. 



sm a 

 A graphical iteration method will be used to solve (98). First we solve 

 <Pi{a) sin a — €(p2{o-) sin a — /i = (99) 



