Skip to content
Snippets Groups Projects
Commit 4d99132a authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Missing ' in the comoving Gadget-SPH lagrangian.

parent 3501b3d6
No related branches found
No related tags found
1 merge request!590Added derivation of comoving Euler equations to cosmology theory document.
...@@ -35,7 +35,7 @@ respectively. Following \cite{Peebles1980} (ch.7), we introduce the ...@@ -35,7 +35,7 @@ respectively. Following \cite{Peebles1980} (ch.7), we introduce the
gauge transformation $\Lag \rightarrow \Lag + \frac{d}{dt}\Psi$ with gauge transformation $\Lag \rightarrow \Lag + \frac{d}{dt}\Psi$ with
$\Psi \equiv \frac{1}{2}a\dot{a}\mathbf{r}_i^2$ and obtain $\Psi \equiv \frac{1}{2}a\dot{a}\mathbf{r}_i^2$ and obtain
\begin{align} \begin{align}
\Lag &= \frac{1}{2}m_ia^2 \dot{\mathbf{r}}_i^2 - \Lag &= \frac{1}{2}m_ia^2 \dot{\mathbf{r}}_i'^2 -
\frac{1}{\gamma-1}m_iA_i'\left(\frac{\rho_i'}{a^3}\right)^{\gamma-1} \frac{1}{\gamma-1}m_iA_i'\left(\frac{\rho_i'}{a^3}\right)^{\gamma-1}
-\frac{\phi'}{a},\\ -\frac{\phi'}{a},\\
\phi' &= a\phi + \frac{1}{2}a^2\ddot{a}\mathbf{r}_i'^2,\nonumber \phi' &= a\phi + \frac{1}{2}a^2\ddot{a}\mathbf{r}_i'^2,\nonumber
......
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Please register or to comment