- #1
Bruno Tolentino
- 97
- 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?
[tex]
\begin{bmatrix}
\frac{d x}{dt}\\
\frac{d y}{dt}
\end{bmatrix}
=
\begin{bmatrix}
\alpha_{11} & \alpha_{12} \\
\alpha_{21} & \alpha_{22}
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}[/tex]
[tex]
\begin{bmatrix}
A_{11} & A_{12} \\
A_{21} & A_{22}
\end{bmatrix}
\begin{bmatrix}
\frac{d^2 x}{dt^2}\\
\frac{d^2 y}{dt^2}
\end{bmatrix}
+
\begin{bmatrix}
B_{11} & B_{12} \\
B_{21} & B_{22}
\end{bmatrix}
\begin{bmatrix}
\frac{d x}{dt}\\
\frac{d y}{dt}
\end{bmatrix}
+
\begin{bmatrix}
C_{11} & C_{12} \\
C_{21} & C_{22}
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
=
\begin{bmatrix}
0\\
0
\end{bmatrix}[/tex]
[tex]
\begin{bmatrix}
\frac{d x}{dt}\\
\frac{d y}{dt}
\end{bmatrix}
=
\begin{bmatrix}
\alpha_{11} & \alpha_{12} \\
\alpha_{21} & \alpha_{22}
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}[/tex]
[tex]
\begin{bmatrix}
A_{11} & A_{12} \\
A_{21} & A_{22}
\end{bmatrix}
\begin{bmatrix}
\frac{d^2 x}{dt^2}\\
\frac{d^2 y}{dt^2}
\end{bmatrix}
+
\begin{bmatrix}
B_{11} & B_{12} \\
B_{21} & B_{22}
\end{bmatrix}
\begin{bmatrix}
\frac{d x}{dt}\\
\frac{d y}{dt}
\end{bmatrix}
+
\begin{bmatrix}
C_{11} & C_{12} \\
C_{21} & C_{22}
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
=
\begin{bmatrix}
0\\
0
\end{bmatrix}[/tex]