1.5.G.sagews

from sympy import *
from sympy import N as Num

# pie is better than pi
pie = 2*pi

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

# quantity = symbol:
a, F = var("a, F")

# pie = 2 pi
# pie/8 = 45 deg
alpha = pie/8

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

# unknowns:
A_h, A_v, B, C_h, C_v, S = var("A_h, A_v, B, C_h, C_v, S")
unknowns = [A_h, A_v, B, C_h, C_v, S]

c = cos(alpha)

# Equilibrium conditions:
eq1 = Eq(0, A_h + C_h)
eq2 = Eq(0, A_v + C_v - S - F)
eq3 = Eq(0, a*C_v - 2*a*S - 3*a*F)

eq4 = Eq(0, -C_h - B*c)
eq5 = Eq(0, -C_v + S + B*c)
eq6 = Eq(0, - a*S + 2*a*C_v + a*C_h)

eqns = [eq1,eq2,eq3,eq4,eq5,eq6]

# Solve:
sol = solve(eqns, unknowns)
pprint(sol)

--- User input ----------------------- --- a: ------------------------------- ___ 3*F -F 3*\/ 2 *F -3*F -3*F {A_h: ---, A_v: ---, B: ---------, C_h: -----, C_v: 0, S: -----} 2 2 2 2 2