\documentclass[a4j,12pt]{jarticle}
\usepackage{Dennou6}
\usepackage{times}
\Ddate{2001 $BG/(B 8 $B7n(B 23 $BF|(B}
\Dauthor{$B>.9b(B $B@5;L(B}

\markright{$B%O%I%l!<=[4D$NI}(B}

\begin{document}
\setlength{\parskip}{3mm}

\section*{$B%O%I%l!<=[4D$NI}(B}

\subsection*{$B0^EY7PEY:BI87O$G$N3Q1?F0NLJ]B8(B}

$u$ $B$rEl@>Iw(B, $a$ $B$rCO5eH>7B(B, $\Omega $ $B$rCO5e$N<+E>3QB.EY(B, $\varphi $ 
$B$r0^EY$H$9$k$H(B, $M$ $B$r;~E@<4J}8~$N3Q1?F0NL$O(B

\[
 M = a \cos \varphi ( u + a\Omega \cos \phi ),
\]

$B$H$J$k(B. 

$B3Q1?F0NL$rJ]B8$7$F@VF;$+$i0^EY(B $\varphi $ $B$^$GJQ0\$7$?$H$9$k$H(B,

\[
 a \cos \varphi ( u + a\Omega \cos \phi ) = a^{2}\Omega
\]

$B$3$l$h$j(B,

\begin{equation}
 u(\varphi) = \frac{a\Omega}{\cos \varphi} - a\Omega \cos \varphi
            = a\Omega \frac{\sin ^{2}\varphi}{\cos \varphi}
 \Deqlab{$B3Q1?F0NLJ]B8E*El@>Iw(B}
\end{equation}

\subsection*{$B0^EY7PEY:BI87O$G$N29EYIwJ?9U(B}

$B0^EY7PEY:BI87O$NFnKLJ}8~$N1?F0J}Dx<0$+$i(B, $B29EYIwJ?9U$O$*$*$^$+$K(B

\begin{equation}
 \frac{2\Omega u\sin \varphi + u^{2}\tan \varphi /a}{H} = 
 -\frac{g}{aT_{0}}\DP{T}{\varphi}.
 \Deqlab{$B29EYIw(B}
\end{equation}

$B$HI=$5$l$k(B. $B$3$3$G(B $H$ $B$OBg5$$N8|$5(B, $T$ $B$O29EY(B, $T_{0}$ $B$O$=$N0^EY7PEY(B
$BJ?6QCM$G$"$k(B.

\subsection*{$B%O%I%l!<=[4D$NI}(B}

\Deqref{$B29EYIw(B}$B<0$K(B\Deqref{$B3Q1?F0NLJ]B8E*El@>Iw(B}$B<0$rBeF~$7(B, $\varphi =0$
$B$+$i(B $\varphi _{0}$ $B$^$G@QJ,$9$k(B.

\begin{eqnarray*}
 2\Omega u\sin \varphi + \frac{u^{2}\tan \varphi}{a} &=&
 2a\Omega ^{2} \frac{\sin ^{3}\varphi }{\cos \varphi} + 
               a \Omega ^{2}\frac{\sin ^{4}\varphi}{\cos ^{2}\varphi}
                            \frac{\sin \varphi}{\cos \varphi} \\
 &=& 
 a\Omega ^{2} \frac{\sin ^{3}\varphi }{\cos \varphi} \left[
               2 + \frac{\sin ^{2}\varphi}{\cos ^{2}\varphi} \right] \\
 &=&
 a\Omega ^{2} \frac{\sin ^{3}\varphi }{\cos ^{3}\varphi} \left[
               1 + \cos ^{2}\varphi \right] \\
 &=&
 a\Omega ^{2} \frac{ 1 - \cos ^{4}\varphi }{\cos ^{3}\varphi} \sin \varphi
\end{eqnarray*}

$B$h$j(B, \Deqref{$B29EYIw(B}$B<0:8JU$N@QJ,$O(B

\begin{eqnarray*}
 \int _{0}^{\varphi _{0}}
  \frac{a\Omega ^{2}}{H} 
  \frac{ 1 - \cos ^{4}\varphi }{\cos ^{3}\varphi} \sin \varphi \Dd \varphi 
&=& 
 \int _{1}^{\cos \varphi _{0}}
  \frac{a\Omega ^{2}}{H} 
  \frac{ 1 - t^{4}}{t^{3}} \Dd t \\
&=& 
  \frac{a\Omega ^{2}}{2H}\tan ^{2}\varphi _{0}.
\end{eqnarray*}

\Deqref{$B29EYIw(B}$B<01&JU$N@QJ,$r(B

\[
 \int _{0}^{\varphi _{0}}
 -\frac{g}{aT_{0}}\DP{T}{\varphi}\Dd \varphi
 =  -\frac{g}{aT_{0}}\Delta T(\varphi _{0}),
\]

$B$H$9$k$H(B, 

\[
a\Omega ^{2} \frac{1}{2H}\tan ^{2}\varphi _{0} = 
-\frac{g}{aT_{0}}\Delta T(\varphi _{0})
\]

$B$3$l$h$j(B

\begin{equation}
\Delta T(\varphi _{0}) = \frac{a^{2}\Omega ^{2}T_{0}}{2gH}
 \tan ^{2}\varphi _{0}.
\Deqlab{$B%O%I%l!<=[4D$NI}(B}
\end{equation}

$\Delta T$ $B$O3Q1?F0NLJ]B8E*$J;R8aLL=[4D$,B8:_$9$k>l9g$K5vMF$5$l$kFnKL29(B
$BEY:9(B, $\varphi _{0}$ $B$O@VF;$+$i$=$N29EY:9$KC#$9$k0^EY$G$"$k(B.

$BCOI=LL29EY$N0^EYJ,I[$,M?$($i$l$F$$$k>l9g(B, \Deqref{$B%O%I%l!<=[4D$NI}(B}$B<0(B
$B$+$i%O%I%l!<=[4D$NI}$rBg$^$+$K8+@Q$b$k$3$H$,$G$-$k(B.

\end{document}