Plugs of Water 2
Last time we derived the following Lagragian \begin{equation} L = \sum_{i}^{N}\left( \frac 12 m_i \dot x_i^2 - m_i x_i \right) +F x_1 -\sum_{i=2}^{N}\frac{q}{\gamma - 1} \frac{1}{(x_{i+1} - x_i - \ell_{i})^{ \gamma - 1 }} \end{equation} Where all the the parameters and variables are unitless. Let’s a deeper look at this Lagragian. One thing that stands out is the form of the air compression energy. It only depends on the difference of position variables of the form $x_{i} - x_{i-1}$....