\vspace{0.5cm}
\noindent
{\bf 4. $B:BI8(B}

$B;0BN>WFM$N>l=j$KF3F~$5$l$?ITJQ=89g$K$D$$$F5DO@$9$kA0$K!"FsBN>WFM$K$h$kFC0[@-$r<h$j=|$-$?$$!%<!@a$G$O50F;$rFsBN>WFM$r1[$($FCF@-H?H/$H$7$F1dD9$9$k$D$b$j$G$"$k!%7W;;$r3Z$K$9$k$?$a$K?7$7$$:BI87O$rF3F~$7!"J}Dx<0(B(3.8)$B$r(B$R^4$$B>e$N%Y%/%H%k>l$KJQ49$9$k!%(B

$BD>@~>e$K(B$q_1 < q_2 < q_3$$B$N=g=x$GJB$s$@N3;R$+$iOC$r;O$a$h$&!%$3$l$i$NN3;R$OG$0U$NFsBN>WFM$N$"$H$G$b=g=x$rJ]$D!%$f$($KG$0U$N50F;$K1h$C$F=g=x$OJ]B8$5$l$k!%(B
$$ \begin{array}{l}
 {\bf S}_0 = \{ {\bf s} \in {\bf S}: s_1 < s_2 < s_3 \}, \\
 {\bf S}_1 = \{ {\bf s} \in {\bf S}: s_1 \leq s_2 \leq s_3 \}, \\
 {\bf T}_0 = \{ ({\bf s}, {\bf u}) \in {\bf T}: 
{\bf s} \in {\bf S}_0 \}, \\
 {\bf T}_1 = \{ ({\bf s}, {\bf u}) \in {\bf T}: 
{\bf s} \in {\bf S}_1 \}, 
   \end{array}
$$
$B$H$*$/!%$^$?(B${\bf a} = (a_1, a_2, a_3)$$B$*$h$S(B${\bf b} = (b_1, b_2, b_3)$$B$O(B${\bf S}$$B>e$G(B$a_1 = a_2 < a_3$$B$*$h$S(B$b_1 < b_2 = b_3$$B$J$k0l0U$NE@$H$9$k!%(B${\bf S}_1$$B$O(B${\bf S}$$B>e$N(B${\bf a}$$B$*$h$S(B${\bf b}$$B$rC<E@$H$9$kJD6h4V$G$"$j!"0lJ}(B${\bf S}_0$$B$OBP1~$9$k3+6h4V$G$"$k!%C<E@$OFsBN>WFM$KBP1~$9$k!%(B(Fig.1$B;2>H(B.)

${\bf T}_1$$B$O%3%s%Q%/%H$J6h4V$H<B<4$H$ND>@Q$KF1Aj$G$"$k$3$H$KCm0U$9$k!%(B$R^6$$B$NItJ,=89g$h$j(B$R^2$$B$NItJ,=89g$r<h$j07$&J}$,ET9g$,$h$$$N$G!"<!$K(B$[-1,1] \times R^1$$B$H(B${\bf T}_1$$B$N4V$NHyJ,F1Aj$rDj5A$9$k!%(B
$$ \begin{array}{ll}
     A_1 = \left[
       \begin{array} {ccc}
         1 & 1 & 1 \\
         1 & 1 & 1 \\
         1 & 1 & 1
       \end{array}   \right], &
     A_2 = \left[
       \begin{array} {ccc}
         0 & 1 & -1 \\
         -1 & 0 & 1 \\
         1 & -1 & 0
       \end{array}   \right] ,
   \end{array}
$$
$B$H$*$-!"<!$rDj5A$9$k!%(B
$$
A = \frac{\displaystyle 1}{\displaystyle m_1 + m_2 + m_3} A_1 M + 
  ( \frac{\displaystyle m_1m_2m_3}{\displaystyle m_1 + m_2 + m_3} )^{1/2} M^{-1} A_2. 
$$
$B=iEyE*$J7W;;$h$j!"(B$A$$B$,0J2<$N@-<A$r;}$D$3$H$,<($;$k!%(B
$$ \begin{array}{lcc}
 A^T M A = M, & & 
   \end{array}        \eqno(4.1) 
$$
$$ \begin{array}{lcc}
 A: {\bf Q} \rightarrow {\bf Q},  & &   
   \end{array}        \eqno(4.2) 
$$
$$ \begin{array}{lcc}
{\bf q}^T M A {\bf q} = 0 & {\rm if} & {\bf q} \in {\bf Q},  
   \end{array}        \eqno(4.3)
$$
$$ \begin{array}{lcc}
A^2 {\bf q} = - {\bf q} & {\rm if} &   {\bf q} \in {\bf Q}, 
   \end{array}        \eqno(4.4)
$$
$$ \begin{array}{lcc}
{\bf a}^T A^T M {\bf b} > 0. 
   \end{array}        \eqno(4.5)
$$
${\bf Q}$$B$,(B$M$$B$K$h$C$FM6F3$5$l$kFb@Q$r;}$F$P!"(B$A$$B$O(B${\bf Q}$$B$K$*$1$k(B$90^{\circ}$$B$N2sE>$G$"$j!"(B${\bf a}$$B$H(B${\bf b}$$B$OC10LD9$5$r;}$A!"(B$\{ {\bf a}, A{\bf a} \}$$B$O(B${\bf Q}$$B$ND>8r4p$G$"$k!%$7$?$,$C$F(B
$$
 {\bf b} = ({\bf a}^T M {\bf b}) {\bf a} + 
           ({\bf a}^T A^T M {\bf b}) A {\bf a},     \eqno(4.6)
$$
$B$rF@$k!%(B

${\bf a}^T M {\bf b}$$B$O<ANL$N$_$K0MB8$9$kDj?t$G$"$k$3$H!"$^$?(B
$$
  0 < {\bf a}^T M {\bf b} < 1,
$$
$B$KCm0U$9$k!%(B$\lambda$$B$O(B
$$
  \cos 2 \lambda = {\bf a}^T M {\bf b},              \eqno(4.7)
$$
$B$rK~$?$9:G>.$N@5?t$H$9$k!%(B$\lambda$$B$O<ANL(B$m_1, m_2$$B$*$h$S(B$m_3$$B$N$_$K0MB8$9$kDj?t$G$"$k$3$H$KCm0U$9$k!%$3$N$H$-<0(B(4.6)$B$*$h$S@-<A(B(4.7)$B$+$i(B
$$
  {\bf b} = ( \cos 2 \lambda ) {\bf a} + (\sin 2 \lambda ) A {\bf a}, 
 \eqno(4.8)
$$
$B$G$"$k!%$5$FG$0U$N<B?t(B$s$$B$KBP$7$F(B
$$
  S(s) = (\sin 2 \lambda)^{-1}[(\sin \lambda (1-s)){\bf a} + 
(\sin \lambda (1+s)){\bf b}],   \eqno(4.9)
$$
$B$rDj5A$9$k!%(B

\vspace{0.3cm}
\noindent
{\bf $BJdBj(B4.1.} $S: [-1,1] \rightarrow  {\bf S}_1$$B$O<B2r@OE*HyJ,F1Aj$G$"$C$F<!$rK~$?$9!%(B
$$
  S'(s) = \lambda A S(s).          \eqno(4.10)
$$

\vspace{0.3cm}
\noindent
\underbar{ $B>ZL@(B.} $BL@$i$+$K(B$S$$B$O<B2r@OE*$G$"$C$F!"(B$S(-1) = {\bf a}$$B$*$h$S(B$S(1) = {\bf b}$$B$G$"$k!%(B${\bf a}, {\bf b} \in {\bf Q}$$B$G$"$k$+$i!"$9$Y$F$N<B?t(B$s$$B$KBP$7$F(B$S(s) \in {\bf Q}$$B$G$"$k!%<0(B(4.8)$B$*$h$S$$$/$i$+$N;03QK!$N7W;;$+$i(B
$$
  S(s) = (\cos \lambda (1+s)){\bf a} + 
(\sin \lambda (1+s)) A{\bf a},   \eqno(4.11)
$$
$B$,F@$i$l$k!%@-<A(B(4.1)$B$*$h$S(B(4.3)$B$+$i(B$S(s)^T M S(s) = 1$$B$,F@$i$l!"$h$C$F$9$Y$F$N(B$s$$B$KBP$7$F(B$S(s) \in {\bf S}$$B$G$"$k!%$3$3$G@-<A(B(4.4)$B$H8x<0(B(4.11)$B$r;H$C$F<0(B(4.10)$B$,F3$-=P$;$k!%;D$C$F$$$k$N$O(B$S: [-1,1] \rightarrow {\bf S}_1$$B$,0lBP0l$G$"$k$3$H$r<($9$3$H$@$1$G$"$k!%$J$<$J$i!"$3$N$H$-<0(B(4.10)$B$*$h$S5U4X?tDjM}$+$i(B$S$$B$,<B2r@OE*HyJ,F1Aj$G$"$k$3$H$,$$$($k$+$i$G$"$k!%(B
$$
  S(s) = (S_1(s), S_2(s), S_3(s)),
$$
$B$H$*$/!%$3$N$H$-(B
$$ \begin{array}{l}
 S_2(s) - S_1(s) = 
       (\sin 2 \lambda)^{-1}(b_2 - b_1) \sin \lambda (1+s), \\
 S_3(s) - S_2(s) = 
       (\sin 2 \lambda)^{-1}(a_3 - a_2) \sin \lambda (1-s), \\
 S_3(s) - S_1(s) = 
       (\sin 2 \lambda)^{-1}
[(b_2 - b_1) \sin \lambda (1+s) + (a_3 - a_2) \sin \lambda (1-s) ],
   \end{array}         \eqno(4.12)
$$
$B$rF@$k!%(B$0 < \lambda < \pi/4$$B$+$D(B$s \in [-1,1]$$B$G$"$k$+$i!"(B$\sin \lambda (1+s)$$B$H(B$\sin \lambda (1-s)$$B$O5U$rM-$7!">e$N?t$O(B3$B$D$H$b@5$G$"$k!%$7$?$,$C$F(B$S: [-1,1] \rightarrow {\bf S}$$B$O0lBP0l$G(B$s \in [-1,1]$$B$KBP$7$F(B$S(s) \in {\bf S}_1$$B$G$"$k!%(B\hfill $\Box$

\vspace{0.3cm}
$B<!$K4X?t(B$S$$B$r;H$C$F!"(B$({\bf s}, {\bf u}) \in T_1$$B$KBP$7$F?7$7$$JQ?t$rDj5A$7$h$&!%(B
$$ \begin{array}{l}
  s = S^{-1}({\bf s}), \\
  u = {\bf s}^T A^T {\bf u},
   \end{array}
$$
$B$H$*$/!%$3$N$H$-(B$s \in [-1,1]$$B$*$h$S(B$u \in R^1$$B$G$"$k!%(B
$$
  {\cal R} = [0, \infty) \times R^1 \times [-1,1] \times R^1,
$$
$B$H$*$1$P!"<B2r@OE*HyJ,F1Aj(B
$$
  {\cal R} \rightarrow [0, \infty) \times R^1 \times {\bf T}_1 : 
(r, v, s, u) \mapsto (r, v, (S(s), uMAS(s))),      \eqno(4.13)
$$
$B$rDj5A$7$?$3$H$K$J$k!%$3$N<LA|$r(B$[0,\infty) \times R^1 \times (-1,1) \times R^1$$B$K@)8B$9$l$P!"(B$[0, \infty) \times R^1 \times {\bf T}_0$$B$N>e$X$NHyJ,F1Aj$H$J$k$3$H$KCm0U$7$h$&!%(B

$B<!$K<0(B(3.8)$B$GM?$($i$l$k%Y%/%H%k>l$rJQ49$9$k!%(B
$$
  V: (-1,1) \rightarrow R^1: s \mapsto U(S(s)),
$$
$B$H$*$/!%>-Mh$N$?$a$K!"<0(B(4.12)$B$rMQ$$$F$-$A$s$H=q$1$P(B
$$ \begin{array}{ll}
 V(s) = \sin 2 \lambda 
  & \left[ \frac{\displaystyle m_1m_2} 
         {\displaystyle (b_2-b_1) \sin \lambda (1+s)} \ + 
    \frac{\displaystyle m_2m_3} 
         {\displaystyle (a_3-a_2) \sin \lambda (1-s)} + \right. \\ 
  & \left. \frac{\displaystyle m_1m_3} 
         {\displaystyle (b_2-b_1) \sin \lambda (1+s) + 
                       (a_3-a_2) \sin \lambda (1-s) } \ \right] .
   \end{array}                      \eqno(4.14)
$$
$B<0(B(4.10)$B$K$h$j!"$3$N<LA|$NHyJ,$,7W;;$G$-$F(B
$$
  V'(s) = \lambda DU(S(s)) A S(s).       \eqno(4.15)
$$
$BJQ49(B(4.13)$B$GDj5A$5$l$k?7$7$$JQ?t$G$O!"%(%M%k%.!<4X78(B(3.5)$B$O(B
$$
  \frac{1}{2} (u^2 + v^2) - V(s) = rh,    \eqno(4.16)
$$
$B$H$J$k!%0lJ}1?F0J}Dx<0(B(3.8)$B$O(B
$$ \begin{array}{l}
\displaystyle 
 \frac{dr}{dt'} = rv, \\
\displaystyle 
 \frac{dv}{dt'} = \displaystyle \frac{1}{2} v^2 + u^2 - V(s), \\
\displaystyle 
 \frac{ds}{dt'} = \displaystyle \lambda^{-1} u, \\
\displaystyle 
 \frac{du}{dt'} = \displaystyle - \frac{1}{2} vu + \lambda^{-1} V'(s),
   \end{array}       \eqno(4.17)
$$
$B$H$J$k!%(B

$B>e$N<0$O(B${\cal R}$$B>e$KFC0[@-$r;}$D%Y%/%H%k>l$rDj5A$9$k!%FC0[@-$O(B$s = \pm 1$$B$N$H$-@8$8$k!%%Y%/%H%k>l$OJQ49(B(4.13)$B$K$h$j!"<0(B(3.8)$B$GM?$($i$l$k(B$[0,\infty) \times R^1 \times {\bf T}_1$$B>e$N%Y%/%H%k>l$HHyJ,F1Aj$G$"$k!%$@$+$i(B$\{ r=0 \}$$B$O;0BN>WFM$KBP1~$7!"(B$\{ s = \pm 1 \}$$B$OFsBN>WFM$KBP1~$9$k!%$$$^(B$q_1 \leq q_2 \leq q_3$$B$N>l9g$K@)8B$7$F$$$k$3$H$KCm0U$7$h$&!%$7$?$,$C$F5/$3$jF@$kFsBN>WFM$ON3;R(B1$B$H(B2($s=-1$)$B$N4V!"$^$?$ON3;R(B2$B$H(B3($s=+1$)$B$N4V$N$b$N$N$_$G$"$k!%<!@a$G$O!"<0(B(4.17)$B$r(B${\cal R}$$B>e$NFC0[@-$J$7$N%Y%/%H%k>l$XJQ49$9$k$3$H$K$h$C$FFsBN>WFM$r1[$($F50F;$r1dD9$9$k!%(B

\vspace{0.5cm}
\noindent
{\bf 5. $BFsBN>WFM$N@5B'2=(B}

$B#3<!85$N;0BNLdBj$K$*$$$F$b50F;$,FsBN>WFM$r1[$($F1dD9$G$-$k$3$H$O$h$/CN$i$l$F$$$k!%(BSundman[14]$B$O$3$N$h$&$J1dD9$N$?$a$N2r@OE*5;=Q$rM?$($F$$$k!%(BEaston[4,5]$B$O0LAjE*5;=Q$rM?$(!"$=$l$rMQ$$$FJ?LL;0BNLdBj$N@5B'2=%(%M%k%.!]B?MMBN$r5-=R$7$?!%$3$3$G$O(BSundman$B$N$K;w$?JQ49$r;H$C$F%(%M%k%.!<B?MMBN>e$N$9$Y$F$NFsBN>WFM$rBg0hE*$K@5B'2=$9$k!%@5B'2=$OJ*M}E*$K$OCF@-H?H/$KBP1~$9$k!%(B

$s \in (-1,1)$$B$KBP$7$F(B
$$
  W(s) = 2(1-s^2) V(s),         \eqno(5.1)
$$
$B$rDj5A$9$k!%(B(4.14)$B<0$r;H$C$F$3$N4X?t$r=q$-49$($k$H!"(B
$$
  W(s) = 2 \lambda ^{-1} \sin 2 \lambda [W_1(s) + W_2(s) + W_3(s)]. 
\eqno(5.2)
$$
$B$3$3$G(B
$$ \begin{array}{l}
 W_1(s) = \displaystyle 
\frac{m_1m_2 (1-s)}{(b_2-b_1) S n (\lambda (1+s))}, \\  
 W_2(s) = \displaystyle 
\frac{m_2m_3 (1+s)}{(a_3-a_2) S n (\lambda (1-s))},  \\ 
 W_3(s) = \displaystyle 
\frac{\lambda m_1m_3 (1-s^2)} 
  {(b_2-b_1) \sin \lambda (1+s) + (a_3-a_2) \sin \lambda (1-s) }. 
   \end{array}                     
$$
$B$?$@$7(B
$$
  S n (x) = \displaystyle \frac{\sin x}{x}.
$$
$Sn(x)$$B$O(B$[0, \pi/2]$$B>e$N@5$N<B2r@O4X?t$K3HD%$G$-$k$7!"(B$0< \lambda < \pi/4$$B$G$"$k$+$i!"(B$W_1$$B$H(B$W_2$$B$O(B$[-1, 1]$$B>e$N<B2r@O4X?t$H$J$k!%$@$+$i!"(B
$W$$B$O(B$[-1, 1]$$B>e$N@5$N<B2r@O4X?t$K3HD%$G$-$k!%$=$l$rF1$8$/(B$W$$B$GI=$o$=$&!%(B

$B$5$F?7$7$$JQ?t(B
$$
  w = (1-s^2) W(s)^{-1/2} u,
$$
$B$rDj5A$9$k!%$9$J$o$A!"<B2r@O4X?t(B
$$ \begin{array}{rl}
[0, \infty) \times R^1 \times (-1,1) \times R^1 
 & \rightarrow [0,\infty) \times R^1 \times (-1,1) \times R^1 : \\
(r,v,s,w) & \mapsto (r,v,s,(1-s^2)^{-1} W(s)^{1/2} w),   
   \end{array}               \eqno(5.3)
$$
$B$rDj5A$9$k!%%(%M%k%.!]4X78<0(B(4.16)$B$O(B
$$
  w^2 + s^2 - 1 + (1-s^2)^2 W(s)^{-1} (v^2 -2rh) = 0,  \eqno(5.4)
$$
$B$H$J$j!"1?F0J}Dx<0(B(4.17)$B$O<!$N$h$&$K$J$k!%(B
$$ \begin{array}{l} 
\displaystyle 
 \frac{dr}{dt'} = rv, \\
\displaystyle 
\frac{dv}{dt'} = \displaystyle 
\frac{1}{2} v^2 - \frac{W(s)}{2(1-s^2)} (1- \frac{2w^2}{1-s^2}), \\
\displaystyle 
\frac{ds}{dt'} = \displaystyle \frac{W(s)^{1/2}}{\lambda (1-s^2)} w, \\ 
\displaystyle 
\frac{dw}{dt'} = \displaystyle - \frac{1}{2} vw + 
 \frac{W(s)^{1/2}}{\lambda (1-s^2)} 
\left[ s(1- \frac{2w^2}{1-s^2}) + \frac{1}{2} \frac{W'(s)}{W(s)} 
(1-s^2 - w^2) \right].
   \end{array}
$$

$BFsBN>WFM$K$h$kFC0[@-$O(B$s = \pm 1$$B$G@8$8$k!%;~4VJQ49$r9T$$!"$^$?%(%M%k%.!<4X78<0$r;H$C$F$3$NFC0[@-$r<h$j=|$1$k!%$^$:;~4VJQ49(B
$$
  dt' = \lambda (1-s^2) W(s)^{-1/2} d \tau,           \eqno(5.5)
$$
$B$r9T$J$&!%$3$N$H$->e$NJ}Dx<0$O<!$N$h$&$K$J$k!%(B
$$ \begin{array}{l}
\displaystyle 
 \frac{dr}{d \tau} = 
     \displaystyle \frac{\lambda (1-s^2)}{W(s)^{1/2}} rv, \\
\displaystyle 
 \frac{dv}{d \tau} = \displaystyle 
\frac{\lambda}{2} 
\left[ \frac{(1-s^2)}{W(s)^{1/2}} v^2 - W(s)^{1/2} 
(1 - \frac{2w^2}{1-s^2}) \right], \\
\displaystyle 
 \frac{ds}{d \tau} = w, \\
\displaystyle 
 \frac{dw}{d \tau} = s \left( 1 - \frac{2w^2}{1-s^2} \right) + 
 \frac{1}{2} \frac{W'(s)}{W(s)} (1-s^2 - w^2) - 
 \frac{\lambda (1-s^2)}{2 W(s)^{1/2}} vw.  
  \end{array}                     \eqno(5.6)
$$
$B%(%M%k%.!<4X78<0(B(5.4)$B$+$i(B
$$
\displaystyle 
  1 -  \frac{2 w^2}{(1-s^2)} = 
       \displaystyle \frac{2(1-s^2)}{W(s)} (v^2 - 2rh) -1,
$$
$B$,F@$i$l$k!%$3$l$r(B(5.6)$B<0$KBeF~$7$F<!$,F@$i$l$k!%(B
$$ \begin{array}{l}
\displaystyle 
 \frac{dr}{d \tau} = \displaystyle 
 \frac{\lambda (1-s^2)}{W(s)^{1/2}} rv, \\
\displaystyle 
 \frac{dv}{d \tau} = \displaystyle 
\frac{\lambda}{2} W(s)^{1/2} 
\left[ 1 - \frac{(1-s^2)}{W(s)} (v^2 - 4rh) \right], \\
\displaystyle 
 \frac{ds}{d \tau} = w, \\
\displaystyle 
 \frac{dw}{d \tau} = \displaystyle 
- s + \frac{2s (1-s^2)}{W(s)} (v^2 - 2rh) + 
 \frac{1}{2} \frac{W'(s)}{W(s)} (1-s^2 - w^2) -  
\frac{\lambda (1-s^2)}{2 W(s)^{1/2}} vw.    
   \end{array}                     \eqno(5.7)
$$
$B$3$l$i$NJ}Dx<0$O(B${\cal R}$$B>e$K<B2r@O%Y%/%H%k>l$rDj5A$9$k!%(B

$B3F<B?t(B$h$$B$KBP$7$F(B
$$
  N(h) = \{ (r,v,s,w) \in {\cal R}: (5.4)$B$,@.$jN)$D(B \},
$$
$B$H$*$/!%I=<0(B(5.4)$B$N8{G[$O(B$N(h)$$B>e$G%<%m$K$J$i$J$$$+$i!"(B$N(h)$$B$O(B${\cal R}$$B$N#3<!85<B2r@OE*ItJ,B?MMBN$G$"$k!%(B(5.4)$B<0$OJQ49$5$l$?%O%_%k%H%s4X?t$G$"$k$+$i!"(B$N(h)$$B$O%Y%/%H%k>l(B(5.6)$B$N$b$H$GITJQ$G$"$k!%$7$?$,$C$F(B(5.6)$B<0$O(B$N(h)$$B>e!"$=$l$,Dj5A$5$l$F$$$kItJ,$N>e$G$N%Y%/%H%k>l$G$"$C$F!"(B(5.7)$B$O(B(5.6)$B$r(B$N(h)$$B$NA4BN$K3HD%$7$?$b$N$G$"$k!%(B

$B$3$N;~E@$G!"$$$^$^$G2f!9$,$J$7F@$?$3$H$r354Q$7$F$_$h$&!%(B
$$ \begin{array}{l}
  N_3(h) = \{ (r,v,s,w) \in N(h): r=0 \}, \\
  N_2(h) = \{ (r,v,s,w) \in N(h): s= \pm 1 \}, \\
  N_1(h) = N(h) - (N_3(h) \cup N_2(h)),
   \end{array}
$$
$B$H$*$/!%3F8GDj$7$?<B?t(B$h$$B$KBP$7$FB?MMBN(B${\bf M}(h)$$B>e$KDj5A$5$l$?%Y%/%H%k>l$+$i;O$a$?!%<!!9$HJQ49(B(3.1)$B!"(B(3.4)$B!"(B(4.13)$B!"$*$h$S(B(5.3)$B$r$[$I$3$7$?!%$3$l$iJQ49$N9g@.$K$h$jKd$a9~$_(B${\bf M}(h) \rightarrow N(h)$$B$rDj5A$9$k!%;v<B!"$3$NKd$a9~$_$O(B$N_1(h)$$B$N>e$X$N<B2r@OE*HyJ,F1Aj$G$"$k!%;~4VJQ49(B(3.7)$B$H(B(5.5)$B$GDj5A$5$l$k<\EYJQ49$N8e$K!"(B${\bf M}(h)$$B>e$N%Y%/%H%k>l(B(2.3)$B$O(B$N_1(h)$$B>e$N%Y%/%H%k>l(B(5.7)$B$X$H0\$k!%$H$3$m$,!"$3$N?7$7$$%Y%/%H%k>l$O(B$N(h)$$B>e$N<B2r@OE*%Y%/%H%k>l$X$H3HD%$G$-$k!%(B$N_2(h)$$B$NE@$X$N3HD%$OFsBN>WFM$N@5B'2=$KBP1~$9$k!%(B$N_3(h)$$B$NE@$X$N3HD%$O;0BN>WFME@$NITJQ6-3&$r!VE=$j$D$1$k!W$3$H$KBP1~$9$k!%(B${\bf M}(h)$$B>e$NG$0U$N50F;$O(B$N_1(h)$$B>e$NG$0U$N50F;$X$H0\$5$l$k!%$7$+$7!"(B$M(h)$$B>e$NFsBN>WFM$G=*$o$k50F;$O$$$^$d(B$N_2(h)$$B$NE@$rDL$C$F1dD9$5$l$k!%(B${\bf M}(h)$$B>e$N;0BN>WFM$G=*$o$k50F;$O$$$^$d8:B.$5$l!"(B$N_3(h)$$B$KA26aE*$K6a$E$/!%(B

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$$
  dt = \frac{\displaystyle r^{3/2}}{\displaystyle 1+r^{3/2}} dt',
$$
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