tasmet/doc/gas_spring.lyx
J.A. de Jong @ vulgaris b1495f4e12 Added documentation as-is
2016-11-11 23:25:44 +01:00

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#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
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\language english
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\use_package amsmath 1
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\index Index
\shortcut idx
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\end_header
\begin_body
\begin_layout Standard
\begin_inset Formula $K=\frac{\partial F}{\partial x}=S_{l}\frac{\partial p}{\partial x}=S_{l}\frac{\partial p}{\partial\rho}\frac{\partial\rho}{\partial x}=S_{l}c_{0}^{2}$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $\rho=\rho_{0}\frac{V_{0}}{V}$
\end_inset
,
\begin_inset Formula $V=V_{0}+S_{l}x$
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula $\frac{\partial\rho}{\partial x}=-S_{l}\frac{\rho_{0}}{V_{0}}$
\end_inset
\end_layout
\begin_layout Standard
Such that
\end_layout
\begin_layout Standard
\begin_inset Formula $K=-S_{l}^{2}\frac{\rho_{0}c_{0}^{2}}{V_{0}}=-S_{l}^{2}\frac{p_{0}}{\gamma V_{0}}$
\end_inset
\end_layout
\end_body
\end_document