- #1
sergiokapone
- 302
- 17
A solution of equations of motion for charged particle in a uniform magnetic field are well known (##r = const##, ## \dot{\phi} = const##). But if I tring to solve this equation using only mathematical background (without physical reasoning) I can't do this due to entaglements of variables. What trick should I know?
\begin{align}
\ddot{r} - r\dot{\phi}^2 &= \frac{q}{m} r\dot{\phi}B\\
r \ddot{\phi} + 2\dot{r}\dot{\phi} &= -\frac{q}{m}\dot{r}B
\end{align}
\begin{align}
\ddot{r} - r\dot{\phi}^2 &= \frac{q}{m} r\dot{\phi}B\\
r \ddot{\phi} + 2\dot{r}\dot{\phi} &= -\frac{q}{m}\dot{r}B
\end{align}