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Commit cae356db authored by BoB's avatar BoB
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corrected typo

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...@@ -28,12 +28,12 @@ ...@@ -28,12 +28,12 @@
\draw (cart.center) -- (mass1) node[midway,xshift=2mm,yshift=5mm] (mid1) {}; \draw (cart.center) -- (mass1) node[midway,xshift=2mm,yshift=5mm] (mid1) {};
\draw[draw=black,fill=white] (mass1.center) circle (.15cm); \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] \pic["$\theta_1$", draw=black, ->, angle eccentricity=1.15, angle radius=2.2cm]
{angle = upp--cart--mass1}; {angle = upp--cart--mass1};
\draw (cart.center) -- (mass2) node[midway,xshift=1mm,yshift=3mm] (mid2) {}; \draw (cart.center) -- (mass2) node[midway,xshift=1mm,yshift=3mm] (mid2) {};
\draw[draw=black,fill=white] (mass2.center) circle (.15cm); \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 [draw, ->, angle eccentricity=1] {angle = upp--cart--mass2};
\pic["$\theta_2\;$", draw=black, ->, angle eccentricity=1.25, angle radius=1.2cm] \pic["$\theta_2\;$", draw=black, ->, angle eccentricity=1.25, angle radius=1.2cm]
{angle = upp--cart--mass2}; {angle = upp--cart--mass2};
...@@ -43,7 +43,7 @@ ...@@ -43,7 +43,7 @@
\caption{Two pendulums on a moving cart} \caption{Two pendulums on a moving cart}
\end{center} \end{center}
\end{figure} \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} \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)\\ 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 V &= m_1gl_1 c_1 + m_2gl_2c_2
......
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