RocketWorkbench/rocketworkbench/Documentation/gba/star/html/images.tex

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\begin{document}
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\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline767}%
$ L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline771}%
$ r_2$%
\lthtmlinlinemathZ
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\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap463}%
\includegraphics[height=5in]{img/variable.ps}%
\lthtmlpictureZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay779}%
$\displaystyle w$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay780}%
$\displaystyle =$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay781}%
$\displaystyle r_1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay783}%
$\displaystyle r_2$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay785}%
$\displaystyle R$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay787}%
$\displaystyle \eta$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay789}%
$\displaystyle \varepsilon$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay791}%
$\displaystyle N$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap471}%
\includegraphics[height=4in]{img/mainstar.ps}%
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\stepcounter{section}
{\newpage\clearpage
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$ w_x$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline802}%
$ r_1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline804}%
$ R-w+w_x$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline806}%
$ (R-w+w_x)(\pi/N - \varepsilon)$%
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{\newpage\clearpage
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$ a$%
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{\newpage\clearpage
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$ (r_1+w_x)a$%
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{\newpage\clearpage
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{\newpage\clearpage
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$ x + y$%
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{\newpage\clearpage
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$\displaystyle b + z$%
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{\newpage\clearpage
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$\displaystyle = (R-w-r_1)\sin{\varepsilon}$%
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{\newpage\clearpage
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$\displaystyle x$%
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{\newpage\clearpage
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$\displaystyle = (r_1+w_x)\tan{\eta}$%
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$\displaystyle \cos{\eta}$%
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$\displaystyle = \frac{r_1+w_x}{z}$%
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{\newpage\clearpage
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$\displaystyle \sin{\eta}$%
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$\displaystyle = \frac{b}{y}$%
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$\displaystyle = \frac{(R-w-r_1)\sin{\varepsilon} -     \frac{r_1+w_x}{\cos{\eta}}}{y}$%
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{\newpage\clearpage
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$\displaystyle L = y + x$%
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$\displaystyle = (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} -                \frac{r_1+w_x}{\cos{\eta}\sin{\eta}} +               (r_1+w_x)\tan{\eta}$%
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$\displaystyle \sin^2{\eta} -1$%
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$\displaystyle = -\cos^2{\eta}$%
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$\displaystyle \tan{\eta}$%
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$\displaystyle = \frac{1}{\tan{(\frac{\pi}{2}-\eta)}}$%
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\begin{displaymath}\begin{split}   L &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} +               (r_1+w_x)\left[              \frac{\sin^2{\eta}-1}{\cos{\eta}\sin{\eta}} \right]\\        &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} +               (r_1+w_x)\left[ \frac{-\cos{\eta}}{\sin{\eta}} \right]\\        &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} +               (r_1+w_x)\left[ \frac{-1}{\tan{\eta}} \right]\\        &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} -               (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\\  \end{split}\end{displaymath}%
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{\newpage\clearpage
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{\newpage\clearpage
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$\displaystyle = (r_2-wx)(\frac{\pi}{2}-\eta)$%
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$\displaystyle x = \frac{r_2-wx}{\tan{\eta}}$%
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{\newpage\clearpage
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$ 0 < w_x < r_2$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath864}%
\begin{displaymath}\begin{split}   \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                   (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}                + (r_2-w_x)(\frac{\pi}{2}-\eta) \\                 & \quad - (r_2-wx)\tan{(\frac{\pi}{2}-\eta)}\\                 &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                   (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+r_2)\tan{(\frac{\pi}{2}-\eta)}                + (r_2-w_x)(\frac{\pi}{2}-\eta)\\    \end{split}\end{displaymath}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay866}%
$\displaystyle \frac{\delta S}{\delta w_x} = 2N\left[ \frac{\pi}{N} - \varepsilon + a -   \frac{\pi}{2} + \eta \right]$%
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{\newpage\clearpage
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$\displaystyle a = \frac{\pi}{2} - \eta + \varepsilon$%
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{\newpage\clearpage
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$\displaystyle \frac{\delta S}{\delta w_x} = 2\pi$%
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\stepcounter{subsection}
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\lthtmldisplayA{displaymath877}%
\begin{displaymath}\begin{split}   \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) +                  (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\                  & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\\   \end{split}\end{displaymath}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath879}%
\begin{displaymath}\begin{split}    \frac{\delta S}{\delta w_x} &= 2N\left[ \frac{\pi}{N} -\varepsilon +                                   a - \tan{(\frac{\pi}{2} - \eta)} \right]\\                                 &= 2N\left[ \frac{\pi}{2} - \eta +                                   \frac{\pi}{N} - \tan{(\frac{\pi}{2}                                   - \eta)} \right]\\    \end{split}\end{displaymath}%
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{\newpage\clearpage
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$ \eta$%
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{\newpage\clearpage
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$ N$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline885}%
$ \varepsilon$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay887}%
$\displaystyle \frac{\delta S}{\delta w_x} = 0 = \frac{\pi}{2} - \eta +                                    \frac{\pi}{N} - \tan{(\frac{\pi}{2}                                    - \eta)}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay893}%
$\displaystyle \eta = \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)} + \frac{\pi}{2}$%
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{\newpage\clearpage
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$ \pi/N$%
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{\newpage\clearpage
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$ \eta < \pi/N$%
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{\newpage\clearpage
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$ \varepsilon < \pi/N$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline936}%
$ w_x = Y*$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay940}%
$\displaystyle \frac{S}{2N} = (R-w+w_x)(\frac{\pi}{N}-\varepsilon) +                 (r_1+w_x)\left[ \varepsilon +                \arcsin{(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}}) \right]$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath942}%
\begin{displaymath}\begin{split} \frac{\delta S}{\delta w_x} &= 2N \biggl[ \frac{\pi}{N}  +        \arcsin{\biggl(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}\biggr)} - \\        &\quad  \frac{w_x(R-w-r_1)\sin{\varepsilon}}{(r_1+w_x)^2\sqrt{1-\frac{(R-w-r_1)^2\sin^2{\varepsilon}}{(r_1+w_x)^2}}} \biggr]\\  \end{split}\end{displaymath}%
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{\newpage\clearpage
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$\displaystyle Y* = (R-w-r_1)\frac{\sin{\varepsilon}}{\cos{\eta}} - r_1 = w$%
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{\newpage\clearpage
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$\displaystyle \sin{\varepsilon} = \frac{w+r_1}{R-w-r_1}\cos{\eta}$%
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{\newpage\clearpage
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$ w$%
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\stepcounter{subsection}
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$\displaystyle c^2 = a^2 + b^2 - 2ab\cos{\theta}$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath967}%
\begin{displaymath}\begin{split} \frac{S}{2N} = (r_1+w_x) \biggl[ & \varepsilon +       \arcsin{\biggl(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}\biggr)}       - \pi\\        & \quad + \arccos{\biggl(\frac{(r_1+w_x)^2+(R-r_1-w)^2-R^2}{2(r_1+w_x)(R-r_1-w)}\biggr)}       \biggr]\\  \end{split}\end{displaymath}%
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$ 3 inch$%
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$ N=6$%
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{\newpage\clearpage
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$ \eta >
\pi/N$%
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{\newpage\clearpage
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$\displaystyle N = 6$%
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{\newpage\clearpage
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$\displaystyle \eta = 33.53 deg$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay992}%
$\displaystyle \varepsilon = 30 deg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline998}%
$ r_1 = 1/16 in$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1004}%
$\displaystyle w = 0.500$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap617}%
\includegraphics[]{img/res.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap625}%
\includegraphics[height=4in]{img/perimeter.ps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}

\end{document}