<content> <p> Functions </p> </content>

0644e5c3-99d0-43e8-b635-d26d19f26584 26 8 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Data

Cable length

L 13 :

Number of nodes

N 12 :

δL L N 1 + / :

Segment length

Weight per unit length

gc 5 :

mg gc L * N / :

Initial weight of each node

Number of segments is \[REGION[d23e5b2ec8524b959718c58457fe9a1b]]\

N 1 +

Segment lengths

i 1 N 1 + (range :

L0 i el δL :

Node weights

j 1 N range :

Mg0 i el mg :

Support separation

X0 10 :

Height difference

Y0 7 :

Cable car weight

G 20 :

Add cable car weight to p'th node

p 5 :

Mg0 p el Mg0 p el G + :

Mg0.sum Mg0 i el i 1 N sum :

Total weight

Y Y0 X0 / :

L L0 X0 / :

Mg Mg0 Mg0.sum / :

Scale lengths to X0 and weights to Mg0sum

X 1 :

Functions

<content> <p> Functions </p> </content>

T α F i 1 N range F i el T i 1 + el α i 1 + el sin * T i el α i el sin * - Mg i el - : F i N + el T i 1 + el α i 1 + el cos * T i el α i el cos * - : 21 line for F N N + 1 + el L k el α k el cos * k 1 N 1 + sum X - : F N N + 2 + el L k el α k el sin * k 1 N 1 + sum Y - : F 41 line :

Vertical force balance

Horizontal force balance

Horizontal distances must match

Vertical distances must match

Jacobian

T α J i 12 N * (range j 1 N 1 + (range J i j el T α F i el T j el diff : J i j N 1 + (+ el T α F i el α j el diff : 21 line for 11 line for j 1 N 1 + (range J 2 N * 1 + j el T α F 2 N * 1 + el T j el diff : J 2 N * 1 + j N 1 + (+ el T α F 2 N * 1 + el α j el diff : J 2 N * 2 + j el T α F 2 N * 2 + el T j el diff : J 2 N * 2 + j N 1 + (+ el T α F 2 N * 2 + el α j el diff : 41 line for J 31 line :

Initial guesses for tensions and angles

i 1 N 1 + (range T i el Mg j el j 1 i sum : 11 line for

i 1 N 1 + (range α i el i N 1 + / π 3 / * : 11 line for

Newton Raphson iterations

tol 106 -^:

err 1 :

steps 0 :

maxsteps 10 :

err tol > (steps maxsteps < (& steps steps 1 + : s T α stack : fn T α F : jn T α J : δ jn 1 -^fn * (: T s δ - (1 N 1 + (range el : α s δ - (N 2 + (2 N * 2 + (range el : err T α F norme : 81 line while

err 4.54993734 107 -^*

steps 4

Calculate x and y coordinates of nodes

i 1 N 1 + (range :

δx i el L i el α i el cos * :

δy i el L i el α i el sin * :

k 1 N 1 + (range x k el X0 δx j el j 1 k sum * : y k el X0 δy j el j 1 k sum * : 21 line for

xw x p el x p el 21 mat :

yw y p el y p el 1 - 21 mat :

Plot node coordinates line and cable car posirtion!

x y 10 + augment xw yw 10 + augment x p el y p el 9 + augment 3 1 sys

x p el 4.87

Compares with 4.871 in Val Ochkov's original.