11 $B?tCM@QJ,(B

$BHyJ,J}Dx<0$r?tCM@QJ,$9$k$K$O!"HyJ,J}Dx<0$r:9J,J}Dx<0$G6a;w$9$k!#(B

$$m\frac{d^2\vec{r}_{i}(t)}{dt^2} = \vec{F}_{i}(x,t)$$ (119)

$BNc!'%Y%k%l$NJ}K!(B

$$\frac{d^2}{dt^2}\vec{r}_{i} \rightarrow \frac{1}{(\Delta t)^2}\left\{\vec{r}_{i}(t+\Delta t)- 2\vec{r}_{i}(t)+\vec{r}_{i}(t-\Delta t) \right\}$$ (120)

$$\frac{d}{dt}\vec{r}_{i} \rightarrow \frac{1}{(\Delta t)^2}\left\{\vec{r}_{i}(t+\Delta t)-\vec{r}_{i}(t-\Delta t) \right\}$$ (121)

$$m_{i} \frac{d^2\vec{r}_{i}}{dt^2} = \vec{F}_{i}$$ (122)

$$\downarrow$$

$$\left \{ \begin{array}{rr} \vec{r}_{i}(t+\Delta t) & \;=\;\: 2... ...)-\vec{r}_{i}(t-\Delta t)\right\} \qquad\qquad $BB.EY:BI8(B \end{array} \right.$$ (123)

$B;~9o!'(B     $t=n\Delta t \quad (n=1,2,3,\cdots)$

$B=i4|>r7o(B
$B%Y%k%lK!$G$O(B

$B$N$h$&$KA22=<0$,$G$-$F$$$k$N$G!"=i4|G[CV$+$i(B1$B%9%F%C%WL\$r5a$a$k<0$OM?$($i$l$F(B $B$$$J$$!#(B1$B%9%F%C%WL\$NM?$(J}$K$b9)IW$,I,MW$G$"$k!#(B
$B%Y%k%lK!$rMQ$$$k$K$O=i4|G[CV$@$1$G$J$/(B $t=\Delta t$ $B$G$N0LCV:BI8$bI,MW!#0l$D$NJ}K!$H$7$F(B

$$\vec{r}_{i}(\Delta t) = \vec{r}_{i}(0)+ \Delta t \vec{v}_{i}(0)+\frac{(\Delta t)^2}{2M_i} \vec{F}_{i}(0)$$ (125)

$B$J$I$rMQ$$$F(B $t=\Delta t$ $B$N%G!<%?$r:n$k$3$H$,$G$-$k!#$3$NJ}K!$,I,$:$7$bNI$$J}K!(B $B$G$O$J$$!#=i4|2aDx$r@53N$K7W;;$7$?$$>l9g$O!"(B $\vec{r}_{i}(\Delta t)$ $B$N7W;;$K(B $BBP$7$FJL$N7W;;J}K!$r9)IW$9$kI,MW$,$"$k!#(B

$BH/E8!'(B $B%Y%k%l$NJ}K!(B($B>\:Y(B)
$BJ,;RF0NO3X$GMQ$$$i$l$kBeI=E*$J

$$r_i(t+\Delta t) = 2r_i(t)-r_i(t-\Delta t)+ \frac{(\Delta t)^2}{m}F_i(t)+o\left((\Delta t)^4\right)$$ (126)

$$v_i(t) = \frac{1}{2(\Delta t)}\left\{r_i(t+\Delta t)- r_i(t-\Delta t)\right\}+o\left((\Delta t)^2\right)$$ (127)

$B$[$\F1$8?t$r0z$-;;$9$k$H!"M-8z?t;z$N7eMn$A$,5/$3$k!#$=$3$G!"(B

$$\Delta r_i(t+\Delta t) \equiv r_i(t+\Delta t)-r_i(t)$$ (128)

$B$H$*$/$H!"<0(B(126)$B$+$i!"(B

$$r_i(t+\Delta t)-r_i(t) = r_i(t)-r_i(t-\Delta t)+\frac{(\Delta t)^2}{m}F_i(t)$$ (129)

$B$H=q$1$k!#$=$3$G!"%Y%k%lK!$N:9J,2=<0$O!"

$$\Delta r_i(t+\Delta t) = \Delta r_i(t)+ \frac{(\Delta t)^2}{m}F_i(t)$$ (130)

$$r_i(t+\Delta t) = r_i(t)+\Delta r_i(t+\Delta t)$$ (131)

$$v_i(t) = \frac{1}{2(\Delta t)}\left\{\Delta r_i(t+\Delta t)+ \Delta r_i(t)\right\}$$ (132)

$B:BI8$NJQ2=J,(B $\Delta r_i(t)$ $B$@$1$r7W;;$7$F$f$/$N$G!"F1DxEY$N?t$N0z$-;;(B $B$K$h$k7eMn$A$rKI$0$3$H$,$G$-$k!#(B

$B7W;;5!$K$O!"(B ${\Delta r_i(t)}$ $B$r5-21$5$;$F$*$/!#;~9o(B$t$ $B$G$N:BI8$O!"(B

$$r_i(t) = r_i(t-\Delta t) + \Delta r_i(t)$$ (133)

$$= r_i(t-2\Delta t)+\Delta r_i(t-\Delta t)+\Delta r_i(t)$$ (134)

$$= \cdots$$ (135)

$$= r_i(0)+\sum_{k=1}^{n\Delta t}\Delta r_i(k\Delta t)$$ (136)

$B$HI=$5$l$k!#(B $r_i(t)$ $B$rJL$K5-21$5$;$F$*$-!"NO$N7W;;$KMQ$$$k!#(B

$BB.EY%Y%k%lK!(B$B$N>l9g(B
$B$rM?$($F(B $F_i(t)$ $B$O(B$r_i(t)$ $B$rMQ$$$F7W;;(B

$$\Delta r_i(t+\Delta t) = v_i(t)(\Delta t)+\frac{(\Delta t)^2}{2m}F_i(t)+o\left((\Delta t)^3\right)$$ (137)

$$r_i(t+\Delta t) = r_i(t)+\Delta r_i(t+\Delta t) \qquad\qquad \longrightarrow F_i(t+\Delta t)$B$r7W;;(B$$ (138)

$$\Delta v_i(t+\Delta t) = \frac{(\Delta t)^2}{2m}\left\{ F_i(t+\Delta t)+F_i(t)\right\}+o\left((\Delta t)^3\right)$$ (139)

$$v_i(t+\Delta t) = v_i(t)+\Delta v_i(t+\Delta t)$$ (140)

$BLd!'<0(B(137)-(140)$B$rF3=P$;$h!#(B