Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I wanted to study the behaviour of electrons in a spatially bounded system. I want to have a larger number of electrons, but I took 3 to start with and arrived at this system of coupled equations:

[itex]\begin{align}\begin{bmatrix}

\mathbf{\ddot{x_{1}}}\\ \\

\mathbf{\ddot{x_{2}}}\\ \\

\mathbf{\ddot{x_{3}}}

\end{bmatrix} = \frac{1}{4\pi\epsilon_0} \begin{bmatrix}

\frac{q_1 q_2}{m_1} & \frac{q_1 q_3}{m_1} \\ \\

\frac{q_2 q_1}{m_2} & \frac{q_2 q_3}{m_2} \\ \\

\frac{q_3 q_1}{m_3} & \frac{q_3 q_2}{m_3} \\

\end{bmatrix} \begin{bmatrix}

\frac{\mathbf{r_{12}}}{|r_{12}^{3}|} &

\frac{\mathbf{r_{21}}}{|r_{21}^{3}|} &

\frac{\mathbf{r_{31}}}{|r_{31}^{3}|}\\ \\

\frac{\mathbf{r_{13}}}{|r_{13}^{3}|} &

\frac{\mathbf{r_{23}}}{|r_{23}^{3}|} &

\frac{\mathbf{r_{32}}}{|r_{32}^{3}|}

\end{bmatrix}\end{align}

[/itex]

I'm not sure how to solve it: I've only solved the coupled mass problem by diagonalization, but I had a 2x2 matrix there. What method can I use to solve this system?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Coupled differential equations for charged particles

**Physics Forums | Science Articles, Homework Help, Discussion**