```python
import sympy
from sympy.abc import T, zeta, tau, psi, eta, omega
from sympy import symbols, Matrix
from sympy import MatrixSymbol, Matrix
from sympy import FunctionMatrix, symbols, Lambda, MatMul, Matrix
sympy.init_printing(use_latex="mathjax", fontsize='32pt')
l_s, l_m, T, zeta, tau_r, psi, eta, omega_r, psi_r_beta, u_s_alpha,u_s_beta, \
R_s, sigma, L_s, L_m, psi_r_alpha, i_s_alpha, i_s_beta,P_n, J, M_l\
=symbols('l_s, l_m, T, zeta, tau_r, psi, eta, omega_r, psi_r_beta, u_s_alpha, u_s_beta, R_s, sigma, L_s, L_m, psi_r_alpha, i_s_alpha, i_s_beta,P_n, J, M_l')
```


```python
A = Matrix([[i_s_alpha], [i_s_beta], [psi_r_alpha], [psi_r_beta], [omega_r]])
A
```




$$\left[\begin{matrix}i_{s \alpha}\\i_{s \beta}\\\psi_{r \alpha}\\\psi_{r \beta}\\\omega_{r}\end{matrix}\right]$$




```python
B= Matrix([[-zeta, 0, eta/tau_r, eta*omega_r, 0],
          [ 0, -zeta, -eta*omega_r, eta/tau_r, 0],
          [l_m/tau_r, 0, -1/tau_r, -omega_r, 0],
          [0, l_m/tau_r, omega_r, -1/tau_r, 0],
          [0, 0, 0, 0, 0]])
B
```




$$\left[\begin{matrix}- \zeta & 0 & \frac{\eta}{\tau_{r}} & \eta \omega_{r} & 0\\0 & - \zeta & - \eta \omega_{r} & \frac{\eta}{\tau_{r}} & 0\\\frac{l_{m}}{\tau_{r}} & 0 & - \frac{1}{\tau_{r}} & - \omega_{r} & 0\\0 & \frac{l_{m}}{\tau_{r}} & \omega_{r} & - \frac{1}{\tau_{r}} & 0\\0 & 0 & 0 & 0 & 0\end{matrix}\right]$$




```python
C=Matrix([[1/(sigma*l_s), 0],
         [0, 1/(sigma*l_s)],
         [0, 0],
         [0, 0],
         [0, 0]])
C
```




$$\left[\begin{matrix}\frac{1}{l_{s} \sigma} & 0\\0 & \frac{1}{l_{s} \sigma}\\0 & 0\\0 & 0\\0 & 0\end{matrix}\right]$$




```python
D=Matrix([[u_s_alpha], [u_s_beta]])
D
```




$$\left[\begin{matrix}u_{s \alpha}\\u_{s \beta}\end{matrix}\right]$$




```python
FF=B*A+C*D
FF
```




$$\left[\begin{matrix}\eta \omega_{r} \psi_{r \beta} + \frac{\eta}{\tau_{r}} \psi_{r \alpha} - i_{s \alpha} \zeta + \frac{u_{s \alpha}}{l_{s} \sigma}\\- \eta \omega_{r} \psi_{r \alpha} + \frac{\eta}{\tau_{r}} \psi_{r \beta} - i_{s \beta} \zeta + \frac{u_{s \beta}}{l_{s} \sigma}\\\frac{i_{s \alpha}}{\tau_{r}} l_{m} - \omega_{r} \psi_{r \beta} - \frac{\psi_{r \alpha}}{\tau_{r}}\\\frac{i_{s \beta}}{\tau_{r}} l_{m} + \omega_{r} \psi_{r \alpha} - \frac{\psi_{r \beta}}{\tau_{r}}\\0\end{matrix}\right]$$




```python
F = FF.jacobian(Matrix([i_s_alpha, i_s_beta, psi_r_alpha, psi_r_beta, omega_r]))
F
```




$$\left[\begin{matrix}- \zeta & 0 & \frac{\eta}{\tau_{r}} & \eta \omega_{r} & \eta \psi_{r \beta}\\0 & - \zeta & - \eta \omega_{r} & \frac{\eta}{\tau_{r}} & - \eta \psi_{r \alpha}\\\frac{l_{m}}{\tau_{r}} & 0 & - \frac{1}{\tau_{r}} & - \omega_{r} & - \psi_{r \beta}\\0 & \frac{l_{m}}{\tau_{r}} & \omega_{r} & - \frac{1}{\tau_{r}} & \psi_{r \alpha}\\0 & 0 & 0 & 0 & 0\end{matrix}\right]$$




```python
time=symbols('t^._r')
time
```




$$t^{.}_{r}$$




```python

```

78c7e55e9570b3e93ddb0a0d2ccaa7f46115827b
ipynb
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1. YES
2. YES