- #1
Bruno Tolentino
- 96
- 0
If an ODE of 2nd order like this A y''(x) + B y'(x) + C y(x) = 0 has how physical/electrical interpretation a RLC circuit, so, how is the electrical interpretation of a system of ODE of 1nd and 2nd order?
<br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> \alpha_{11} & \alpha_{12} \\ <br /> \alpha_{21} & \alpha_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}
<br /> \begin{bmatrix}<br /> A_{11} & A_{12} \\ <br /> A_{21} & A_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d^2 x}{dt^2}\\ <br /> \frac{d^2 y}{dt^2}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> B_{11} & B_{12} \\ <br /> B_{21} & B_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> C_{11} & C_{12} \\ <br /> C_{21} & C_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> 0\\ <br /> 0<br /> \end{bmatrix}
<br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> \alpha_{11} & \alpha_{12} \\ <br /> \alpha_{21} & \alpha_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}
<br /> \begin{bmatrix}<br /> A_{11} & A_{12} \\ <br /> A_{21} & A_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d^2 x}{dt^2}\\ <br /> \frac{d^2 y}{dt^2}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> B_{11} & B_{12} \\ <br /> B_{21} & B_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> \frac{d x}{dt}\\ <br /> \frac{d y}{dt}<br /> \end{bmatrix}<br /> +<br /> \begin{bmatrix}<br /> C_{11} & C_{12} \\ <br /> C_{21} & C_{22}<br /> \end{bmatrix}<br /> <br /> \begin{bmatrix}<br /> x\\ <br /> y<br /> \end{bmatrix}<br /> =<br /> \begin{bmatrix}<br /> 0\\ <br /> 0<br /> \end{bmatrix}