1.2.F.sagews

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

# Given symbols:
a, b = var("alpha, beta", real=true)
F1, F2 = var("F1, F2", real=true)

ca = cos(a)
sa = sin(a)
cb = cos(b)
sb = sin(b)

Rx = - F1*ca + F2 *cb
Ry = - F1*sa - F2 *sb

R = Matrix([Rx, Ry])
pprint("\n--- a ------------------------------------")
pprint("\n--- Symbols-------------------------------")
pprint("\nR:")
pprint(R)
Rmag=R.norm()
pprint("\n||R||:")
pprint(Rmag)


pprint("\n--- b ------------------------------------")
pprint("\n--- Quantities ---------------------------")
sublist = {
    a: 60*pi/180, b: 45*pi/180,
    F1: 6*newton, F2: 2*newton
    }

R = R.subs(sublist)
R = R.applyfunc(simplify)
pprint("\nR / N:")
pprint("Exact:")
pprint(R/newton)
# pprint("Latex:")
# pprint(latex(R/newton))
pprint("Rounded:")
pprint(N(R/newton,2))
# pprint(latex(N(R/newton,2)))
Rmagq = Rmag.subs(sublist)
Rmagq = Rmagq.simplify()
pprint("\n||R|| / N:")
pprint("Exact:")
pprint(Rmagq/newton)
# pprint("Latex:")
# pprint(latex(Rmag/newton))
pprint("Rounded:")
pprint(N(Rmagq/newton,2))
# pprint("Latex:")
# pprint(latex(N(Rmag/newton,2)))

pprint("\n--- c ------------------------------------")
gamma = acos(-Ry/Rmag)
pprint("\ngamma:")
gamma=gamma.subs(sublist)
gamma=gamma.simplify()
pprint("Rounded gamma / deg:")
pprint(N(gamma*180/pi,2))
# pprint(latex(N(gamma*180/pi,2)))

pprint("\n--- d ------------------------------------")
ca = F2/F1*cb
ca = ca.subs(sublist)
pprint(ca)
a = acos(ca)
adeg=a*180/pi
adegN =N(adeg,2)
pprint(adegN)

--- a ------------------------------------ --- Symbols------------------------------- R: [-F1*cos(alpha) + F2*cos(beta)] [ ] [-F1*sin(alpha) - F2*sin(beta)] ||R||: ___________________________________________________________________ / 2 2 \/ (F1*sin(alpha) + F2*sin(beta)) + (F1*cos(alpha) - F2*cos(beta)) --- b ------------------------------------ --- Quantities --------------------------- R / N: Exact: [ ___ ] [ -3 + \/ 2 ] [ ] [ ___ ___] [- 3*\/ 3 - \/ 2 ] Rounded: [-1.6] [ ] [-6.6] ||R|| / N: Exact: __________________________ / ___ ___ \/ - 6*\/ 2 + 6*\/ 6 + 40 Rounded: 6.8 --- c ------------------------------------ gamma: Rounded gamma / deg: 13. --- d ------------------------------------ ___ \/ 2 ----- 6 76.