The generalization to multiple coordinates $q_i$ ($i=1,\ldots,n$) is straightforward: \begin{eqnarray} {d \over dt} {\partial L \over \par...

The generalization to multiple coordinates $q_i$ ($i=1,\ldots,n$) is straightforward: \begin{eqnarray} {d \over dt} {\partial L \over \partial \dot{q}_i} - {\partial L \over \partial q_i} = 0 \label{eq:eulerlagrange} \end{eqnarray} \subsubsection{Noether's Theorem} \label{sec:noether} Given a Lagrangian ...