6.3: Going From State Space to Phase Space
- Page ID
- 29563
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Now, the momenta are the derivatives of the Lagrangian with respect to the velocities, \(\begin{equation}
p_{i}=\partial L\left(q_{i}, \dot{q}_{i}\right) / \partial \dot{q}_{i}
\end{equation}\). So, how do we get from a function \(\begin{equation}
L\left(q_{i}, \dot{q}_{i}\right)
\end{equation}\) of positions and velocities to a function of positions and the derivatives of that function L with respect to the velocities?