1.2.G.sagews

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

# Given symbols:
R, a, b = var("R, alpha, beta", real=true)

ta = tan(a)
tb = tan(b)

# Unknowns:
F1x, F1y, F2x, F2y = var("F_{1x}, F_{1y}, F_{2x}, F_{2y}", real=true)

unknowns = [F1x, F1y, F2x, F2y]

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

eq1 = Eq(F1x + F2x, 0)
eq2 = Eq(F1y + F2y, -R)
eq3 = Eq(ta, F1y/F1x)
eq4 = Eq(tb, F2y/F2x)

eqns = [eq1, eq2, eq3, eq4]
sol = solve(eqns, unknowns)

(F1x, F1y) = (sol[F1x], sol[F1y])
(F2x, F2y) = (sol[F2x], sol[F2y])
F1 = Matrix([F1x, F1y])
F2 = Matrix([F2x, F2y])

pprint("\nF1:")
pprint(F1)
# pprint(latex(F1))
pprint("\nF2:")
pprint(F2)
# pprint(latex(F2))

pprint("\n--- b ------------------------------------")
pprint("\n--- Quantities ---------------------------")
sublist = {
    R: S(9)/2*newton,
    a: 45*pi/180, b: 15*pi/180
    }

pprint("S1 and S2:")
for F in [F1, F2]:
    F = F.subs(sublist)
    F /= newton
    pprint("\nComponents / N:")
    pprint("\nExact:")
    pprint(F)
    # pprint(latex(F))
    pprint("\nApprox:")
    pprint(N(F,2))
    # pprint(latex(N(F,2)))

pprint("\n--- c ------------------------------------")
pprint("\n--- Quantities ---------------------------")
for F in [F1, F2]:
    F = F.subs(sublist)
    F /= newton
    pprint("\nNorm = Magnitude / N:")
    F = F.norm()
    pprint(N(F,2))

--- a ------------------------------------ --- Symbols------------------------------- F1: [ -R ] [----------------------] [tan(alpha) - tan(beta)] [ ] [ -R*tan(alpha) ] [----------------------] [tan(alpha) - tan(beta)] F2: [ R ] [----------------------] [tan(alpha) - tan(beta)] [ ] [ R*tan(beta) ] [----------------------] [tan(alpha) - tan(beta)] --- b ------------------------------------ --- Quantities --------------------------- S1 and S2: Components / N: Exact: [ -9 ] [--------------] [ / ___\] [2*\-1 + \/ 3 /] [ ] [ -9 ] [--------------] [ / ___\] [2*\-1 + \/ 3 /] Approx: [-6.1] [ ] [-6.1] Components / N: Exact: [ 9 ] [-------------- ] [ / ___\ ] [2*\-1 + \/ 3 / ] [ ] [ / ___ \] [9*\- \/ 3 + 2/] [---------------] [ / ___\] [ 2*\-1 + \/ 3 /] Approx: [6.1] [ ] [1.6] --- c ------------------------------------ --- Quantities ---------------------------- Norm = Magnitude / N: 8.7 Norm = Magnitude / N: 6.4