Ka'plan 



ll = (1+e) cos 4>, |X = (i+e) sin ^ (89) 

 and with the definitions 



u=|2, v=|i (90) 



U = u sin ^ - V cos ^ (91) 



V = u cos (^ + V sin ^ (92) 



It can be shown that 



and 



U3- V(^3= - (1+^^^ (93) 



V3 + U^5 = €^ (94) 



where the s and t subscripts represent partial derivative operations, 



By considering effects normal and tangential to the cable, the 

 basic dynamic equations can be expressed In the form 



H.[ U^ - V^^] = - T^s + F(l+c) + Wc cos ^ (95) 



|i[ Vt + U<^t] = Tg + G(l+c) - Wc sin <t>. (96) 



In addition the relation 



Is also necessary, so that the basic equations governing the cable 

 dynajnlcs are Eqs. (93) - (97), where the first two relations are 

 basically kinematic. For the steady state case, I.e. neglecting 

 time derivatives, Eqs. (95) and (96) reduce to the same expressions 

 as given In the static equilibrium case. I.e. Eqs. (50) and (51) . 



To solve the quaslUnear partial differential equations given 

 In Eqs. (93) and (97), a linearization procedure can be applied. 

 Defining the expressions 



1064 



