dy = sing ds [4] 
Equations [1], [2], [3], and [4] taken together completely define 
the tension and configuration of the cable when the end concitions T, and ¢, 
are known. 
Equation [1] is immediately integrable to 
T= Ty + Fx [5] 
Eliminating ds from Equations [1] and [2] and substituting f for 
Ewe obtain 
dT _ _—~fcos¢d¢ SISO COR 
T sin?g + fsing ce Pp EIO [6] 
which integrates to give 
1 + fescd ae 
T= ioe C 
1) fiesegy To ony ap 
Substituting this value of T into Equation [2] 
Ridsy _ —(1 + fesed)d¢d _ ese? ddd 
I (1 + f cscg,)(sin?d + fsing) — 1 + fesed, [8] 
This integrates to give 
Rs _ cotd — cotdy 
T. 9 se Pee, [9] 
From Equations [8] and [3] we obtain 
Rdx _ —cscd cotddd (10] 
I 1 + fcscdo 
which gives upon integration 
Re _ csch — cscho 
A SM ap PERE [11] 
From Equations [8] and [4] we obtain 
Rdy _ —esceg dd 
i 1 + fesedy [12] 
which gives upon integration 
: cot p/2 
Jey) cot $o/2 [13] 
i le nnesciay 
