```python
# https://colab.research.google.com/github/kassbohm/wb-snippets/blob/master/ipynb/HTM_03/Selbst/4.3.ipynb

from sympy import *

# Shortcuts:
Ca, Sa, Ct, St = var("cₐ, sₐ, cₜ, sₜ")

#
l, m = var("l, m", positive = True)
a, t = var("α, θ")

ca, sa = cos(a), sin(a)
ct, st = cos(t), sin(t)

sub_list = [
    (ca, Ca),
    (sa, Sa),
    (ct, Ct),
    (st, St),
    ]

R2 = Matrix([
    [ 1, 0,  0  ],
    [ 0, ct, st ],
    [ 0,-st, ct ]
    ])
R1 = Matrix([
    [ ca, 0, -sa ],
    [  0, 1,   0 ],
    [ sa, 0, -ca ]
    ])

R = R2*R1
Rt = R.transpose()

JOt = Matrix([
    [  1, 0, 0 ],
    [  0, 0, 0 ],
    [  0, 0, 1 ]
    ])

JO = Rt*JOt*R

pprint("\nR:")
tmp = R.subs(sub_list)
pprint(tmp)

pprint("\nJO / (ml²/3):")
tmp = JO.subs(sub_list)
pprint(tmp)

# R:
# ⎡ cₐ     0    -sₐ  ⎤
# ⎢                  ⎥
# ⎢sₐ⋅sₜ  cₜ   -cₐ⋅sₜ⎥
# ⎢                  ⎥
# ⎣cₜ⋅sₐ  -sₜ  -cₐ⋅cₜ⎦
#
# JO / (ml²/3):
# ⎡     2     2   2                       2           ⎤
# ⎢   cₐ  + cₜ ⋅sₐ      -cₜ⋅sₐ⋅sₜ  - cₐ⋅cₜ ⋅sₐ - cₐ⋅sₐ⎥
# ⎢                                                   ⎥
# ⎢                          2                        ⎥
# ⎢     -cₜ⋅sₐ⋅sₜ          sₜ           cₐ⋅cₜ⋅sₜ      ⎥
# ⎢                                                   ⎥
# ⎢       2                             2   2     2   ⎥
# ⎣- cₐ⋅cₜ ⋅sₐ - cₐ⋅sₐ  cₐ⋅cₜ⋅sₜ      cₐ ⋅cₜ  + sₐ    ⎦

```

0bcc330cfb86905126e710ae430cf641e3a1bb48
ipynb
Jupyter Notebook
ipynb/HTM_03/Selbst/4.3.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
ipynb/HTM_03/Selbst/4.3.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
ipynb/HTM_03/Selbst/4.3.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
Qwen/Qwen-72B
1. YES
2. YES