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6.3: Going From State Space to Phase Space

Last updated

Dec 30, 2020
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- 6.2: Phase Space
- 6.4: How It's Done in Thermodynamics

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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?

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