```python
from sympy import *

a, q0 = var("a, q0")

Ah, Av, Bh, Bv, Gh, Gv = var("Ah, Av, Bh, Bv, Gh, Gv")

x = var("x")
q1 = q0/3   * x/a
q2 = 2*q0/3 * x/(2*a)
q3 = q0/3

# Resultants:
R1 = integrate( q1, (x, 0,   a) )
R2 = integrate( q2, (x, 0, 2*a) )
R3 = integrate( q3, (x, 0, 2*a) )

x1 = integrate( x*q1, (x, 0,   a) ) / R1
x2 = integrate( x*q2, (x, 0, 2*a) ) / R2
x3 = integrate( x*q3, (x, 0, 2*a) ) / R3

# Print results:
pprint("\nx1, R1:")
pprint(x1)
pprint(R1)
pprint("\nx2, R2:")
pprint(x2)
pprint(R2)
pprint("\nx3, R3:")
pprint(x3)
pprint(R3)

eq1 = Eq(  0, Ah + Gh             )
eq2 = Eq(  0, R1 + Gv - Av        )
eq3 = Eq(  0, 2*R1/3 + Gv + Gh    )
eq4 = Eq(  0, Bh - Gh             )
eq5 = Eq(  0, R2 + R3 - Gv - Bv   )
eq6 = Eq(  0, 2*Gv - R3 - 2*R2/3  )

eqns = [eq1, eq2, eq3, eq4, eq5, eq6]
unks = [Ah, Av, Bh, Bv, Gh, Gv]

sol = solve( eqns, unks)
pprint(sol)
pprint(latex(sol))

# x1, R1:
# 2⋅a
# ───
#  3
# a⋅q₀
# ────
#  6
#
# x2, R2:
# 4⋅a
# ───
#  3
# 2⋅a⋅q₀
# ──────
#   3
#
# x3, R3:
# a
# 2⋅a⋅q₀
# ──────
#   3
# ⎧    2⋅a⋅q₀      13⋅a⋅q₀      -2⋅a⋅q₀       7⋅a⋅q₀      -2⋅a⋅q₀       5⋅a⋅q₀⎫
# ⎨Ah: ──────, Av: ───────, Bh: ────────, Bv: ──────, Gh: ────────, Gv: ──────⎬
# ⎩      3            18           3            9            3            9   ⎭

```

0299c3111109c49436aaa4517c4b059a1f7c2b1f
ipynb
Jupyter Notebook
ipynb/TM_1/5_AL/1.5.L.ipynb
kassbohm/tm-snippets
5e0621ba2470116e54643b740d1b68b9f28bff12
MIT
ipynb/TM_1/5_AL/1.5.L.ipynb
kassbohm/tm-snippets
5e0621ba2470116e54643b740d1b68b9f28bff12
MIT
ipynb/TM_1/5_AL/1.5.L.ipynb
kassbohm/tm-snippets
5e0621ba2470116e54643b740d1b68b9f28bff12
MIT
Qwen/Qwen-72B
1. YES
2. YES