diff --git a/modeling.pdf b/modeling.pdf
index 977cf7a898644f81add749b2b4f5e1d68fdf13ce..190cb6e89baa9357ef590f0464e99cd8533dfa96 100644
Binary files a/modeling.pdf and b/modeling.pdf differ
diff --git a/modeling.tex b/modeling.tex
index a5e2a2a3156b059d0a8fa475edaf7810597adb8e..d3f22747ae228e9cf3d3b222a83907d3d687f153 100644
--- a/modeling.tex
+++ b/modeling.tex
@@ -28,12 +28,12 @@
     
     \draw (cart.center) -- (mass1)  node[midway,xshift=2mm,yshift=5mm] (mid1) {};
     \draw[draw=black,fill=white] (mass1.center) circle (.15cm);
-    \node at (mass1.north) [anchor=south,xshift=1mm,yshift=1mm] { $(x_1,y_1)$};
+    \node at (mass1.north) [anchor=south,xshift=1.5mm,yshift=1mm] { $(x_1,y_1)$};
     \pic["$\theta_1$", draw=black, ->, angle eccentricity=1.15, angle radius=2.2cm]
     {angle = upp--cart--mass1};
     \draw (cart.center) -- (mass2) node[midway,xshift=1mm,yshift=3mm] (mid2) {};
     \draw[draw=black,fill=white] (mass2.center) circle (.15cm);
-    \node at (mass2.north) [anchor=south,xshift=1mm,yshift=1mm] { $(x_2,y_2)$};
+    \node at (mass2.north) [anchor=south,xshift=1.5mm,yshift=1mm] { $(x_2,y_2)$};
     %\pic [draw, ->,  angle eccentricity=1] {angle = upp--cart--mass2};
     \pic["$\theta_2\;$", draw=black, ->, angle eccentricity=1.25, angle radius=1.2cm]
     {angle = upp--cart--mass2};
@@ -43,7 +43,7 @@
 \caption{Two pendulums on a moving cart}
 \end{center}
 \end{figure}
-Two pendulums with lengths $l_1$ and $l_2$ and masses $m_1$ and $m_2$ are mounted on a moving cart with mass $M$, see Figure~\ref{fig01}. Introduce $L = T - V$ where kinetick and potential energies are given by
+Two pendulums with lengths $l_1$ and $l_2$ and masses $m_1$ and $m_2$ are mounted on a moving cart with mass $M$, see Figure~\ref{fig01}. Introduce $L = T - V$ where kinetic and potential energies are given by
 \begin{align}
 T &= \frac{1}{2}M\dot x^2 + \frac{1}{2}m_1(\dot x_1^2 + \dot y_1^2) + \frac{1}{2}m_2(\dot x_2^2 + \dot y_2^2)\\
 V &= m_1gl_1 c_1 + m_2gl_2c_2