- #1

AxiomOfChoice

- 533

- 1

[tex]

\mathcal L = -mc^2 / \gamma - e \vec v \cdot \vec A

[/tex]

in cylindrical coordinates. But isn't this DREADFULLY TERRIBLE, since when I try to compute [tex] \dfrac{d}{dt} \dfrac{\partial \mathcal L}{\partial \dot q_i} [/tex] I'm going to have to take the time derivative of [tex]\gamma[/tex], which takes the form

[tex]

\gamma = \left(1 - \frac{1}{c^2} (\dot r ^2 + r^2 \dot \phi^2 + \dot z^2) \right)^{-1/2}

[/tex]

Am I making this too hard? Please help!