```python
from sympy import *
from sympy.vector import CoordSys3D
N = CoordSys3D('N')
alpha, beta, K, L, ga, gv = symbols("alpha beta K L g_a g_v")
af=Function('a')

init_printing()
```


```python
a = pi / 2 + K * (L / 2 - alpha)


x = (1 / K + ga * cos(gv * a)) * cos(a)
y = beta
z = (1 / K + ga * cos(gv * a)) * sin(a)
```


```python
r = x*N.i + y*N.j + z*N.k

r.subs(pi / 2 + K * (L / 2 - alpha), af(alpha)).subs(K * (L / 2 - alpha), af(alpha)-pi / 2)
```


```python
dr_dalpha = r.diff(alpha)
dr_dalpha.subs(pi / 2 + K * (L / 2 - alpha), af(alpha)).subs(K * (L / 2 - alpha), af(alpha)-pi / 2)
```


```python
dr_dbeta = r.diff(beta)
dr_dbeta
```


```python
A=dr_dalpha.magnitude()
A.subs(pi / 2 + K * (L / 2 - alpha), af(alpha)).subs(K * (L / 2 - alpha), af(alpha)-pi / 2)
```


```python
e_alpha=dr_dalpha / A
e_alpha = e_alpha.subs(pi / 2 + K * (L / 2 - alpha), af(alpha)).subs(K * (L / 2 - alpha), af(alpha)-pi / 2)
e_alpha
```


```python
B=dr_dbeta.magnitude()
B
```


```python
e_beta=dr_dbeta / B
e_beta
```


```python
n_temp = e_alpha.cross(e_beta)
n=n_temp.normalize()
n = n.subs(pi / 2 + K * (L / 2 - alpha), af(alpha)).subs(K * (L / 2 - alpha), af(alpha)-pi / 2)
n = sympify(n)
n
```


```python
e_alpha.diff(alpha)
```


```python
e_alpha.diff(beta)
```


```python
e_beta.diff(alpha)
```


```python
e_beta.diff(beta)
```


```python
n.diff(alpha)
```


```python
n.diff(beta)
```


```python

```

23c3619d6d084c998d7afbf3699e024ce0aaa79c
ipynb
Jupyter Notebook
py/notebooks/draft/Novozilov.ipynb
tarashor/vibrations
fcbadd545e2a8f1ef4b4bff399b396ee5f16924b
MIT
2018-02-05T18:05:08.000Z
2018-02-05T18:05:08.000Z
py/notebooks/draft/Novozilov.ipynb
tarashor/vibrations
fcbadd545e2a8f1ef4b4bff399b396ee5f16924b
MIT
py/notebooks/draft/Novozilov.ipynb
tarashor/vibrations
fcbadd545e2a8f1ef4b4bff399b396ee5f16924b
MIT
Qwen/Qwen-72B
1. YES
2. YES