Based on the original Rocket Workbench on SourceForge in CVS at:
https://sourceforge.net/projects/rocketworkbench
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589 lines
19 KiB
589 lines
19 KiB
\batchmode
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\documentclass[11pt,titlepage]{article}
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\RequirePackage{ifthen}
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\usepackage{amsmath,graphicx}
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\usepackage[dvips]{color}
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\pagecolor[gray]{.7}
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\usepackage[]{inputenc}
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\makeatletter
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\makeatletter
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\count@=\the\catcode`\_ \catcode`\_=8
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\newenvironment{tex2html_wrap}{}{}%
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\catcode`\<=12\catcode`\_=\count@
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\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
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\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
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\expandafter\renewcommand\csname #1\endcsname}%
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\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
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\let\newedcommand\renewedcommand
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\let\renewedenvironment\newedenvironment
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\makeatother
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\let\mathon=$
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\let\mathoff=$
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\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
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\newbox\sizebox
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\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
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\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
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\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
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\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
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\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
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\setlength{\textwidth}{349pt}
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\newwrite\lthtmlwrite
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\makeatletter
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\let\realnormalsize=\normalsize
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\global\topskip=2sp
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\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
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\def\@float{\let\@savefreelist\@freelist\real@float}
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\def\liih@math{\ifmmode$\else\bad@math\fi}
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\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
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\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
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\let\@largefloatcheck=\relax
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\let\if@boxedmulticols=\iftrue
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\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
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\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
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\parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
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\def\phantompar{\csname par\endcsname}\normalsize}%
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\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
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\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
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\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
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\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
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\let\ifinner=\iffalse \let\)\liih@math }%
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\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
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\expandafter\box\next\egroup}%
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\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
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\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize %
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:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
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\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
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\lthtmlmathtype{#1}\lthtmlvboxmathA}%
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\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
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\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
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\let\@savefreelist\@freelist \lthtmlhboxmathB}%
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\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
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\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
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\global\let\@freelist\@savefreelist}%
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\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
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\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
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\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
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\lthtmldisplayA{#1}\let\@eqnnum\relax}%
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\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
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\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
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\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
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\vrule height1.5ex width0pt }%
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\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
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\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
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\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
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\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
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\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
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\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
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\newcommand\lthtmlindisplaymathZ{\egroup %
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\centerinlinemath\lthtmllogmath\lthtmlsetmath}
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\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
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\kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
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\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
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\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
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\kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
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\ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
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\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
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\def\centerinlinemath{%
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\dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
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\advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1
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\dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}
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\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize
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\ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
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\else\expandafter\vss\fi}%
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\providecommand{\selectlanguage}[1]{}%
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\makeatletter \tracingstats = 1
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\providecommand{\Eta}{\textrm{H}}
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\providecommand{\Mu}{\textrm{M}}
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\providecommand{\Alpha}{\textrm{A}}
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\providecommand{\Iota}{\textrm{J}}
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\providecommand{\Nu}{\textrm{N}}
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\providecommand{\Omicron}{\textrm{O}}
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\providecommand{\omicron}{\textrm{o}}
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\providecommand{\Chi}{\textrm{X}}
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\providecommand{\Beta}{\textrm{B}}
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\providecommand{\Kappa}{\textrm{K}}
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\providecommand{\Tau}{\textrm{T}}
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\providecommand{\Epsilon}{\textrm{E}}
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\providecommand{\Zeta}{\textrm{Z}}
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\providecommand{\Rho}{\textrm{R}}
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\begin{document}
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\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
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\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
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\makeatletter
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\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
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\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
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\lthtmltypeout{}%
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\makeatother
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\setcounter{page}{1}
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\onecolumn
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% !!! IMAGES START HERE !!!
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline767}%
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$ L$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline771}%
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$ r_2$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{section}
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\stepcounter{section}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap463}%
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\includegraphics[height=5in]{img/variable.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay779}%
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$\displaystyle w$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay780}%
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$\displaystyle =$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay781}%
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$\displaystyle r_1$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay783}%
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$\displaystyle r_2$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay785}%
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$\displaystyle R$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay787}%
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$\displaystyle \eta$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay789}%
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$\displaystyle \varepsilon$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay791}%
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$\displaystyle N$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap471}%
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\includegraphics[height=4in]{img/mainstar.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{section}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline799}%
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$ w_x$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{subsection}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline802}%
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$ r_1$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline804}%
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$ R-w+w_x$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline806}%
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$ (R-w+w_x)(\pi/N - \varepsilon)$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline810}%
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$ a$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline812}%
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$ (r_1+w_x)a$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap489}%
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\includegraphics[height=5in]{img/starL.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline828}%
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$ x + y$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay829}%
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$\displaystyle b + z$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay830}%
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$\displaystyle = (R-w-r_1)\sin{\varepsilon}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay831}%
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$\displaystyle x$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay832}%
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$\displaystyle = (r_1+w_x)\tan{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay833}%
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$\displaystyle \cos{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay834}%
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$\displaystyle = \frac{r_1+w_x}{z}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay835}%
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$\displaystyle \sin{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay836}%
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$\displaystyle = \frac{b}{y}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay838}%
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$\displaystyle = \frac{(R-w-r_1)\sin{\varepsilon} - \frac{r_1+w_x}{\cos{\eta}}}{y}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay839}%
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$\displaystyle L = y + x$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay840}%
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$\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}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay841}%
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$\displaystyle \sin^2{\eta} -1$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay842}%
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$\displaystyle = -\cos^2{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay843}%
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$\displaystyle \tan{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay844}%
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$\displaystyle = \frac{1}{\tan{(\frac{\pi}{2}-\eta)}}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmldisplayA{displaymath846}%
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\begin{displaymath}\begin{split} L &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} + (r_1+w_x)\left[ \frac{\sin^2{\eta}-1}{\cos{\eta}\sin{\eta}} \right]\\ &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} + (r_1+w_x)\left[ \frac{-\cos{\eta}}{\sin{\eta}} \right]\\ &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} + (r_1+w_x)\left[ \frac{-1}{\tan{\eta}} \right]\\ &= (R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}} - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\\ \end{split}\end{displaymath}%
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\lthtmldisplayZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap507}%
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\includegraphics[height=3in]{img/arc.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay856}%
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$\displaystyle = (r_2-wx)(\frac{\pi}{2}-\eta)$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay858}%
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$\displaystyle x = \frac{r_2-wx}{\tan{\eta}}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline862}%
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$ 0 < w_x < r_2$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmldisplayA{displaymath864}%
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\begin{displaymath}\begin{split} \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) + (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\ & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)} + (r_2-w_x)(\frac{\pi}{2}-\eta) \\ & \quad - (r_2-wx)\tan{(\frac{\pi}{2}-\eta)}\\ &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) + (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\ & \quad - (r_1+r_2)\tan{(\frac{\pi}{2}-\eta)} + (r_2-w_x)(\frac{\pi}{2}-\eta)\\ \end{split}\end{displaymath}%
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\lthtmldisplayZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay866}%
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$\displaystyle \frac{\delta S}{\delta w_x} = 2N\left[ \frac{\pi}{N} - \varepsilon + a - \frac{\pi}{2} + \eta \right]$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_indisplay868}%
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$\displaystyle a = \frac{\pi}{2} - \eta + \varepsilon$%
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\lthtmlcheckvsize\clearpage}
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$\displaystyle \frac{\delta S}{\delta w_x} = 2\pi$%
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\lthtmlcheckvsize\clearpage}
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\stepcounter{subsection}
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\begin{displaymath}\begin{split} \frac{S}{2N} &= (R-w+w_x)(\frac{\pi}{N} - \varepsilon) + (r_1+w_x)a+(R-w-r_1)\frac{\sin{\varepsilon}}{\sin{\eta}}\\ & \quad - (r_1+w_x)\tan{(\frac{\pi}{2}-\eta)}\\ \end{split}\end{displaymath}%
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\begin{displaymath}\begin{split} \frac{\delta S}{\delta w_x} &= 2N\left[ \frac{\pi}{N} -\varepsilon + a - \tan{(\frac{\pi}{2} - \eta)} \right]\\ &= 2N\left[ \frac{\pi}{2} - \eta + \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)} \right]\\ \end{split}\end{displaymath}%
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\lthtmldisplayZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_inline881}%
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$ \eta$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline883}%
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$ N$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline885}%
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$ \varepsilon$%
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\lthtmlinlinemathZ
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay887}%
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$\displaystyle \frac{\delta S}{\delta w_x} = 0 = \frac{\pi}{2} - \eta + \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_indisplay893}%
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$\displaystyle \eta = \frac{\pi}{N} - \tan{(\frac{\pi}{2} - \eta)} + \frac{\pi}{2}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_inline901}%
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$ \pi/N$%
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\lthtmlinlinemathZ
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\lthtmlinlinemathA{tex2html_wrap_inline927}%
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$ \eta < \pi/N$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline929}%
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$ \varepsilon < \pi/N$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{subsection}
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\lthtmlinlinemathA{tex2html_wrap_inline936}%
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$ w_x = Y*$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_indisplay940}%
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$\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]$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmldisplayA{displaymath942}%
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\begin{displaymath}\begin{split} \frac{\delta S}{\delta w_x} &= 2N \biggl[ \frac{\pi}{N} + \arcsin{\biggl(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}\biggr)} - \\ &\quad \frac{w_x(R-w-r_1)\sin{\varepsilon}}{(r_1+w_x)^2\sqrt{1-\frac{(R-w-r_1)^2\sin^2{\varepsilon}}{(r_1+w_x)^2}}} \biggr]\\ \end{split}\end{displaymath}%
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\lthtmldisplayZ
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\lthtmlinlinemathA{tex2html_wrap_indisplay944}%
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$\displaystyle Y* = (R-w-r_1)\frac{\sin{\varepsilon}}{\cos{\eta}} - r_1 = w$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_indisplay946}%
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$\displaystyle \sin{\varepsilon} = \frac{w+r_1}{R-w-r_1}\cos{\eta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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\lthtmlinlinemathA{tex2html_wrap_inline950}%
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$ w$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{subsection}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay965}%
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$\displaystyle c^2 = a^2 + b^2 - 2ab\cos{\theta}$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmldisplayA{displaymath967}%
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\begin{displaymath}\begin{split} \frac{S}{2N} = (r_1+w_x) \biggl[ & \varepsilon + \arcsin{\biggl(\frac{R-w-r_1}{r_1+w_x}\sin{\varepsilon}\biggr)} - \pi\\ & \quad + \arccos{\biggl(\frac{(r_1+w_x)^2+(R-r_1-w)^2-R^2}{2(r_1+w_x)(R-r_1-w)}\biggr)} \biggr]\\ \end{split}\end{displaymath}%
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\lthtmldisplayZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{section}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline970}%
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$ 3 inch$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline984}%
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$ N=6$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline986}%
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$ \eta >
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\pi/N$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay988}%
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$\displaystyle N = 6$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay990}%
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$\displaystyle \eta = 33.53 deg$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay992}%
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$\displaystyle \varepsilon = 30 deg$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_inline998}%
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$ r_1 = 1/16 in$%
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\lthtmlinlinemathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlinlinemathA{tex2html_wrap_indisplay1004}%
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$\displaystyle w = 0.500$%
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\lthtmlindisplaymathZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap617}%
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\includegraphics[]{img/res.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap625}%
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\includegraphics[height=4in]{img/perimeter.ps}%
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\lthtmlpictureZ
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\lthtmlcheckvsize\clearpage}
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\stepcounter{section}
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\end{document}
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