1.3.A.sagews

from sympy import *
from sympy import N as Num

# pie is better than pi
pie = 2*pi

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

# Derived units:
N = kg*m/s/s

print("\n--- User input -----------------------")

symbolic = True
symbolic = False

if symbolic:
    # quantity = symbol:
    alpha = var("alpha")
    F = var("F")
    r = var("r")
else:
    # variable = quantity:
    # derived units:
    N = kg*m/s/s

    # quantity =  factor times unit:
    # pie/12 = 30 deg
    # pie = 2 pi
    alpha = pie/12

    F_val = 5
    F = F_val *N

    r_val = S(2)/10
    r = r_val *m

print("\n--- a: -------------------------------")
# Unknowns:
Ah, Av, S= var("A_h, A_v, S")

ca = cos(alpha)
sa = sin(alpha)

eq1 = Eq(0, Ah + S*sa)
eq2 = Eq(0, Av - S*ca - F)
eq3 = Eq(0, r*F - r*S)

sol = solve([eq1, eq2, eq3], [Ah, Av, S])
pprint(sol)

print("\n--- b: -------------------------------")

eq1 = Eq(0, Ah + S*sa)
eq2 = Eq(0, r*F - r*S)
eq3 = Eq(0, r*sa*Ah - r*ca*Av + r*(1+ca)*F)

sol = solve([eq1, eq2, eq3], [Ah, Av, S])
pprint(sol)

print("\n--- c: -------------------------------")

eq1 = Eq(0, r*F - r*S)
eq2 = Eq(0, r*sa*Ah - r*ca*Av + r*(1+ca)*F)
eq3 = Eq(0, r*Av - r*(1 + ca)*S*ca - r*sa*S*sa)

sol = solve([eq1, eq2, eq3], [Ah, Av, S])
pprint(sol)

--- User input ----------------------- --- a: ------------------------------- / ___ \ -5*kg*m 5*kg*m*\\/ 3 + 2/ 5*kg*m {A_h: --------, A_v: ------------------, S: ------} 2 2 2 2*s 2*s s --- b: ------------------------------- / ___ \ -5*kg*m 5*kg*m*\\/ 3 + 2/ 5*kg*m {A_h: --------, A_v: ------------------, S: ------} 2 2 2 2*s 2*s s --- c: ------------------------------- / ___ \ -5*kg*m 5*kg*m*\\/ 3 + 2/ 5*kg*m {A_h: --------, A_v: ------------------, S: ------} 2 2 2 2*s 2*s s