### apm/tp123.apm

```Model tp123
! Source version 2
! Simple APM canonicalizer version 1.3
! APM backend version 1.1
Parameters
mypi = 4*atan(1)
c2 = 2
c3 = 3
c10 = 10
c20 = 20
c1000 = 1000
c100000 = 100000
g = 980665/c100000
masstot = 50/c1000
rrough = (masstot/((2700 + 19300 + 7860)*(4/c3)*mypi))^(1/c3)
rcage = 1
End Parameters
Variables
x_1 = 1.020462601383630
x_2 = 1.067249920905851
x_3 = -10
x_4 = 1.056302685455057
x_5 = 0.9888734173342870
x_6 = 1.030255683555398
x_7 = 1.002173322039949
x_8 = 0.9898553374984422
x_9 = 1.074494882526627
x_10 = 1.095044196509762
x_11 = -1000
x_12 = 1.089828605856584
obj
End Variables
Intermediates
massa = 2700*(4/c3)*mypi*x_1^3
massg = 19300*(4/c3)*mypi*x_2^3
massi = 7860*(4/c3)*mypi*x_3^3
distac = sqrt(x_4^2 + x_7^2 + (x_10 - rcage)^2)
distgc = sqrt(x_5^2 + x_8^2 + (x_11 - rcage)^2)
distic = sqrt(x_6^2 + x_9^2 + (x_12 - rcage)^2)
distag = sqrt((x_4 - x_5)^2 + (x_7 - x_8)^2 + (x_10 - x_11)^2)
distgi = sqrt((x_5 - x_6)^2 + (x_8 - x_9)^2 + (x_11 - x_12)^2)
distia = sqrt((x_6 - x_4)^2 + (x_9 - x_7)^2 + (x_12 - x_10)^2)
rsumag = x_1 + x_2
rsumgi = x_2 + x_3
rsumia = x_3 + x_1
mf = g*(massa*x_10 + massg*x_11 + massi*x_12)
c_1 = x_8 + x_2/c10
c_2 = massa + massg + massi - masstot
c_3 = (rcage - x_1) - distac
c_4 = (rcage - x_2) - distgc
c_5 = (rcage - x_3) - distic
c_6 = distag - rsumag
c_7 = distgi - rsumgi
c_8 = distia - rsumia
c_9 = (-1)*(x_4 + x_1/c10)
c_10 = x_5 - x_2/c10
c_11 = (-1)*(x_6 + x_3/c10)
c_12 = (-1)*(x_7 + x_1/c10)
c_13 = x_9 - x_3/c10
c_14 = x_1 - x_2/c2
c_15 = x_1 - x_3/c2
c_16 = x_2 - x_1/c2
c_17 = x_2 - x_3/c2
c_18 = x_3 - x_1/c2
c_19 = x_3 - x_2/c2
myminfun = mf
myabsdevnod0_0 = abs(myminfun - 0.003625517252207682)
myreldevnod0_0 = abs(myminfun/0.003625517252207682 - 1)
myabsdevnod0_1 = abs(x_1 - 0.007322215428894107)
myreldevnod0_1 = abs(x_1/0.007322215428894107 - 1)
myabsdevnod0_2 = abs(x_2 - 0.007383190030817839)
myreldevnod0_2 = abs(x_2/0.007383190030817839 - 1)
myabsdevnod0_3 = abs(x_3 - 0.007340627520740361)
myreldevnod0_3 = abs(x_3/0.007340627520740361 - 1)
myabsdevnod0_4 = abs(x_4 + 0.007248606058940914)
myreldevnod0_4 = abs(x_4/0.007248606058940914 + 1)
myabsdevnod0_5 = abs(x_5 - 0.00457274646768661)
myreldevnod0_5 = abs(x_5/0.00457274646768661 - 1)
myabsdevnod0_6 = abs(x_6 + 0.008953401300522358)
myreldevnod0_6 = abs(x_6/0.008953401300522358 + 1)
myabsdevnod0_7 = abs(x_7 + 0.009485008329662611)
myreldevnod0_7 = abs(x_7/0.009485008329662611 + 1)
myabsdevnod0_8 = abs(x_8 + 0.0007383190030817839)
myreldevnod0_8 = abs(x_8/0.0007383190030817839 + 1)
myabsdevnod0_9 = abs(x_9 - 0.005078392253646442)
myreldevnod0_9 = abs(x_9/0.005078392253646442 - 1)
myabsdevnod0_10 = abs(x_10 - 0.007393997445014723)
myreldevnod0_10 = abs(x_10/0.007393997445014723 - 1)
myabsdevnod0_11 = abs(x_11 - 0.007393997445014723)
myreldevnod0_11 = abs(x_11/0.007393997445014723 - 1)
myabsdevnod0_12 = abs(x_12 - 0.007393997445014723)
myreldevnod0_12 = abs(x_12/0.007393997445014723 - 1)
myabsdevnod1_0 = (1/2)*(abs(myabsdevnod0_0 - myabsdevnod0_1) + (myabsdevnod0_0 + myabsdevnod0_1))
myreldevnod1_0 = (1/2)*(abs(myreldevnod0_0 - myreldevnod0_1) + (myreldevnod0_0 + myreldevnod0_1))
myabsdevnod1_2 = (1/2)*(abs(myabsdevnod0_2 - myabsdevnod0_3) + (myabsdevnod0_2 + myabsdevnod0_3))
myreldevnod1_2 = (1/2)*(abs(myreldevnod0_2 - myreldevnod0_3) + (myreldevnod0_2 + myreldevnod0_3))
myabsdevnod1_4 = (1/2)*(abs(myabsdevnod0_4 - myabsdevnod0_5) + (myabsdevnod0_4 + myabsdevnod0_5))
myreldevnod1_4 = (1/2)*(abs(myreldevnod0_4 - myreldevnod0_5) + (myreldevnod0_4 + myreldevnod0_5))
myabsdevnod1_6 = (1/2)*(abs(myabsdevnod0_6 - myabsdevnod0_7) + (myabsdevnod0_6 + myabsdevnod0_7))
myreldevnod1_6 = (1/2)*(abs(myreldevnod0_6 - myreldevnod0_7) + (myreldevnod0_6 + myreldevnod0_7))
myabsdevnod1_8 = (1/2)*(abs(myabsdevnod0_8 - myabsdevnod0_9) + (myabsdevnod0_8 + myabsdevnod0_9))
myreldevnod1_8 = (1/2)*(abs(myreldevnod0_8 - myreldevnod0_9) + (myreldevnod0_8 + myreldevnod0_9))
myabsdevnod1_10 = (1/2)*(abs(myabsdevnod0_10 - myabsdevnod0_11) + (myabsdevnod0_10 + myabsdevnod0_11))
myreldevnod1_10 = (1/2)*(abs(myreldevnod0_10 - myreldevnod0_11) + (myreldevnod0_10 + myreldevnod0_11))
myabsdevnod1_12 = myabsdevnod0_12
myreldevnod1_12 = myreldevnod0_12
myabsdevnod2_0 = (1/2)*(abs(myabsdevnod1_0 - myabsdevnod1_2) + (myabsdevnod1_0 + myabsdevnod1_2))
myreldevnod2_0 = (1/2)*(abs(myreldevnod1_0 - myreldevnod1_2) + (myreldevnod1_0 + myreldevnod1_2))
myabsdevnod2_4 = (1/2)*(abs(myabsdevnod1_4 - myabsdevnod1_6) + (myabsdevnod1_4 + myabsdevnod1_6))
myreldevnod2_4 = (1/2)*(abs(myreldevnod1_4 - myreldevnod1_6) + (myreldevnod1_4 + myreldevnod1_6))
myabsdevnod2_8 = (1/2)*(abs(myabsdevnod1_8 - myabsdevnod1_10) + (myabsdevnod1_8 + myabsdevnod1_10))
myreldevnod2_8 = (1/2)*(abs(myreldevnod1_8 - myreldevnod1_10) + (myreldevnod1_8 + myreldevnod1_10))
myabsdevnod2_12 = myabsdevnod1_12
myreldevnod2_12 = myreldevnod1_12
myabsdevnod3_0 = (1/2)*(abs(myabsdevnod2_0 - myabsdevnod2_4) + (myabsdevnod2_0 + myabsdevnod2_4))
myreldevnod3_0 = (1/2)*(abs(myreldevnod2_0 - myreldevnod2_4) + (myreldevnod2_0 + myreldevnod2_4))
myabsdevnod3_8 = (1/2)*(abs(myabsdevnod2_8 - myabsdevnod2_12) + (myabsdevnod2_8 + myabsdevnod2_12))
myreldevnod3_8 = (1/2)*(abs(myreldevnod2_8 - myreldevnod2_12) + (myreldevnod2_8 + myreldevnod2_12))
myabsdevnod4_0 = (1/2)*(abs(myabsdevnod3_0 - myabsdevnod3_8) + (myabsdevnod3_0 + myabsdevnod3_8))
myreldevnod4_0 = (1/2)*(abs(myreldevnod3_0 - myreldevnod3_8) + (myreldevnod3_0 + myreldevnod3_8))
zmyabsdevmax = myabsdevnod4_0
zmyreldevmax = myreldevnod4_0
End Intermediates
Equations
obj = myminfun
c_1 = 0
c_2 = 0
c_3 >= 0
c_4 >= 0
c_5 >= 0
c_6 >= 0
c_7 >= 0
c_8 >= 0
c_9 >= 0
c_10 >= 0
c_11 >= 0
c_12 >= 0
c_13 >= 0
c_14 >= 0
c_15 >= 0
c_16 >= 0
c_17 >= 0
c_18 >= 0
c_19 >= 0
End Equations
End Model
```

Stephan K.H. Seidl