DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



1171 



(T - PcVc) COS d 





(47) 



+ wA'Ccos" \}/ sin' d + sill" \py''^ sin ^ = 0, (b) 

 dT 



\ 



ds 



+ Dt — w sin 6 = 0, 



(c) 



where A' = CDpdV'^/2, and V is the magnitude of F'. 



In addition, connecting the coordinates ^(s), v(s), and f(s) of a point 

 s along the cable with the angles 6 and \p we have the geometric relation- 

 ships 



dm 



ds 



dr](s) 

 ds 



d^(s) 

 ds 



= cos 6 cos ip, (a) 



= sin 6, (b) 



= —cos 6 sin \p. (c) 



(48) 



Two important general results follow from (47) and (48). For one, if 

 the tangential drag force Dt is negligibly small, (48b) substituted mto 

 equation (47c) yields upon integration 



T = To-\- wr,, (49) 



where To is the tension at r; = 0. Hence, if 77 is measured from the ocean 



"t DIRECTION OF 

 CABLE 



Fig. 27 — Definition of the spherical pohir coordinates 6 and \p and the unit 



vectors t, u, and v. 



