1.2.H.sagews

from sympy.physics.units import *
from sympy import *

# Given symbols:
a, b = var("alpha, beta", real=true)
F1, F2, F3 = var("F1, F2, F3", real=true)
ca = cos(a)
sa = sin(a)
cb = cos(b)
sb = sin(b)

pprint("\n--- a ------------------------------------")
pprint("\n--- Symbols-------------------------------")

F1v = Matrix([-F1*sa, F1*ca])
F2v = Matrix([ F2*cb, F2*sb])
F3v = Matrix([ 0, -F3])
pprint("\nF1, F2, F3:")
for F in [F1v, F2v, F3v]:
    pprint(F)
    # pprint(latex(F))

pprint("\n--- b ------------------------------------")
pprint("\n--- Quantities ---------------------------")
sublist = {
    F1: 4*newton, F2: 2*newton, F3: 3*newton,
    a: 60*pi/180, b: 60*pi/180
    }

for F in [F1v, F2v, F3v]:
    F = F.subs(sublist)
    F /= newton
    pprint(N(F,2))
    # pprint(latex(F))
    # pprint(latex(N(F,2)))

pprint("\n--- c ------------------------------------")
pprint("\n--- Quantities ---------------------------")
pprint("\nNorm = Magnitude / N:")
for F in [F1v, F2v, F3v]:
    F = F.subs(sublist)
    F /= newton
    F = F.norm()
    pprint(F)
    # pprint(latex(F))
    # pprint(latex(N(F,2)))

pprint("\n--- d ------------------------------------")
pprint("\n--- Quantities ---------------------------")
R = F1v + F2v + F3v
pprint(R)
# pprint(latex(N(R,2)))
R = R.norm()
R = R.subs(sublist)
R = R / newton
pprint(latex(N(R,2)))

pprint("\n--- e ------------------------------------")
pprint("\n--- Quantities ---------------------------")
R = F1v + F2v + F3v
Rx = R[0]
R = R.norm()

# cp = cos(phi):
cp = -Rx/R
phi = acos(cp)
phi = phi.subs(sublist)
phideg = phi*180/pi
pprint(N(phideg,2))

--- a ------------------------------------ --- Symbols------------------------------- F1, F2, F3: [-F1*sin(alpha)] [ ] [F1*cos(alpha) ] [F2*cos(beta)] [ ] [F2*sin(beta)] [ 0 ] [ ] [-F3] --- b ------------------------------------ --- Quantities --------------------------- [-3.5] [ ] [2.0 ] [1.0] [ ] [1.7] [ 0 ] [ ] [-3.0] --- c ------------------------------------ --- Quantities --------------------------- Norm = Magnitude / N: 4 2 3 --- d ------------------------------------ --- Quantities --------------------------- [ -F1*sin(alpha) + F2*cos(beta) ] [ ] [F1*cos(alpha) + F2*sin(beta) - F3] 2.6 --- e ------------------------------------ --- Quantities --------------------------- 17.