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ºîÍÑÅÀ¤Ë¤è¤Ã¤ÆƯ¤¤¬°Û¤Ê¤ë¡Ë¤³¤È¤òºÆǧ¼±¤·¤Ê¤±¤ì¤Ð¤Ê¤ê¤Þ¤»¤ó¡¥
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Åù²Á¤ÊÎϤȤϡ©
==============
´Êñ¤ÊÎã¤È¤·¤Æ¡¤¼ÁÎÌ $m_1$, $m_2$ ¤Î¼ÁÅÀ¤ò·Ú¤¤ËÀ¤Ç¤Ä¤Ê¤¤¤À²¼¿Þ¤Î¹äÂΤò¹Í¤¨¤Þ¤¹¡¥
$\bm F_i$, $\bm F_{ik}$ ¤Ï¤½¤ì¤¾¤ì¼ÁÎÌ $m_i$ ¤Î¼ÁÅÀ¤ËƯ¤¯³°ÎÏ¡¤¼ÁÎÌ $m_k$ ¤Î¼ÁÅÀ¤«¤é
¼ÁÎÌ $m_i$ ¤Î¼ÁÅÀ¤ËƯ¤¯ÆâÎϤǤ¹¡¥
.. figure:: pulsar-BoundVector-Fig1.gif
£²¼ÁÅÀ¤ò¤Ä¤Ê¤¤¤À¹äÂÎ
¼ÁÎÌ $m_1$, $m_2$ ¤Î¼ÁÅÀ¤Î°ÌÃÖ¥Ù¥¯¥È¥ë¤ò¤½¤ì¤¾¤ì $\bm r_1$, $\bm r_2$ ¤È¤¹¤ë¤È¡¤ÆâÎϤÏ
<tex>
\bm F_{12} + \bm F_{21} = \bm 0
</tex>
<tex>
(\bm r_1 - \bm r_2) \times \bm F_{12} = \bm 0
</tex>
¤È¤¤¤¦À¼Á¤ò¤â¤Ã¤Æ¤¤¤ë¤Î¤Ç¡¤±¿Æ°ÊýÄø¼°
<tex>
m_i \frac{\mathrm d^2 \bm r_i}{\mathrm d t^2}
= \bm F_i + \sum_{k \neq i}\bm F_{ik}
</tex>
¤«¤é
<tex>
m_1 \frac{\mathrm d^2 \bm r_1}{\mathrm d t^2} +
m_2 \frac{\mathrm d^2 \bm r_2}{\mathrm d t^2} = \bm F_1 + \bm F_2
</tex>
<tex>
\bm r_1 \times m_1 \frac{\mathrm d^2 \bm r_1}{\mathrm d t^2} +
\bm r_2 \times m_2 \frac{\mathrm d^2 \bm r_2}{\mathrm d t^2} +
= \bm r_1 \times \bm F_1 + \bm r_2 \times \bm F_2
</tex>
¤È¤¤¤¦ÆâÎϤò´Þ¤Þ¤Ê¤¤¼°¤¬ÆÀ¤é¤ì¡¤¤³¤ÎÈùʬÊýÄø¼°¤ò²ò¤¯¤³¤È¤Ë¤è¤Ã¤Æ $\bm r_1$, $\bm r_2$
¤òµá¤á¤ë¤³¤È¤¬¤Ç¤¤Þ¤¹ [*]_ ¡¥¹äÂΤα¿Æ°¤ò¹Í¤¨¤ë¤È¤¥â¡¼¥á¥ó¥È¤ò·×»»¤¹¤ë¤Î¤Ï¡¤
Á°µ¤Î $(\bm r_1 - \bm r_2) \times \bm F_{12} = \bm 0$ ¤È¤¤¤¦À©Ìó¤Ë¤è¤ë¤â¤Î¤Ç¤¹¡¥
.. [*] ½Å¿´ $\bm r_{\mathrm G}$ ¤ò
$(m_1 + m_2) \bm r_{\mathrm G} = m_1 \bm r_1 + m_2 \bm r_2$
¤ÇÄêµÁ¤¹¤ë¤È¡¤¼ÁÅÀ¤Î±¿Æ°ÊýÄø¼°¤ÈÎà»÷¤Î
$(m_1 + m_2) \frac{\mathrm d^2 \bm r_{\mathrm G}}{\mathrm d t^2} = \bm F_1 + \bm F_2$
¤¬ÆÀ¤é¤ì¤Þ¤¹¡¥
¤³¤Î¹äÂΤËƯ¤¯ÎϤ¬¤Ä¤ê¹ç¤Ã¤Æ¤¤¤ë¤È¤¤¤¦¤³¤È¤Ï $\bm F_1 + \bm F_2 = \bm 0$,
$\bm r_1 \times \bm F_1 + \bm r_2 \times \bm F_2 = \bm 0$ ¤Ç¤¢¤ë¤³¤È¤ò°ÕÌ£¤·¤Þ¤¹¡¥
¤³¤Î¤³¤È¤«¤é, $\bm F_1, \cdots , m, \cdots , F_m, -\bm F_{m+1}, \cdots , -\bm F_n$ ¤¬
¤Ä¤ê¹ç¤Ã¤Æ¤¤¤ë¤È¤¡¤¤¹¤Ê¤ï¤Á
<tex>
\sum_{i=1}^m \bm F_i = \sum_{i=m+1}^n \bm F_i
</tex>
<tex>
\sum_{i=1}^m \bm r_i \times \bm F_i = \sum_{i=m+1}^n \bm r_i \times \bm F_i
</tex>
¤Ç¤¢¤ë¤È¤, $\bm F_1, \cdots , \bm F_m$ ¤È $\bm F_{m+1}, \cdots , \bm F_n$ ¤Ï
Åù²Á¤Ç¤¢¤ë¤ÈÄêµÁ¤·¤Þ¤¹¡¥¤³¤³¤Ç $\bm r_i$ ¤Ï $\bm F_i$ ¤ÎºîÍÑÅÀ¤Î°ÌÃÖ¥Ù¥¯¥È¥ë¤ò
ɽ¤·¤Æ¤¤¤Þ¤¹¡¥¤³¤Î¤È¤¡¤Ç¤°Õ¤Î $\bm r_0$ ¤Ë¤Ä¤¤¤Æ
<tex>
\sum_{i=1}^m (\bm r_i - \bm r_0) \times \bm F_i
= \sum_{i=m+1}^n (\bm r_i - \bm r_0) \times \bm F_i
</tex>
¤È¤Ê¤ë¤³¤È¤ò³Îǧ¤·¤Æ¤¯¤À¤µ¤¤¡¥
«Çû¥Ù¥¯¥È¥ë¤Îɽ¸½
==================
$\bm r_i$ ¤òºîÍÑÅÀ¤È¤¹¤ëÎÏ $\bm F_i$ ¤ò $\bm F_i(\bm r_i)$ ¤Èɽ¤·¤Æ¤â¡¤
Ä̾ï¤Ï $\bm F_i(\bm r_i) = \bm F_k(\bm r_k)$ ¤Ï $\bm F_i(\bm r_i)$
¤È $\bm F_k(\bm r_k)$ ¤ÎÂ礤µ¤È¸þ¤¤¬Åù¤·¤¤¤È²ò¼á¤µ¤ì¤Þ¤¹¡¥¤³¤Î¤¿¤á¡¤
¿·¤·¤¤µ¹æ $\bm F_i[\bm r_i]$ ¤òÍѤ¤¤Æ
<tex>
\sum_{i=1}^m \bm F_i[\bm r_i] = \sum_{i=m+1}^n \bm F_i[\bm r_i]
</tex>
¤Î°ÕÌ£¤ò
<tex>
\sum_{i=1}^m \bm F_i = \sum_{i=m+1}^n \bm F_i
</tex>
<tex>
\sum_{i=1}^m \bm r_i \times \bm F_i = \sum_{i=m+1}^n \bm r_i \times \bm F_i
</tex>
¤ÇÄêµÁ¤·¤Þ¤¹¡¥¤³¤ÎÄêµÁ¤«¤é¤¿¤À¤Á¤Ë $(\bm r_1 - \bm r_2) \times \bm F_0$ ¤Ê¤é¤Ð
$\bm F_0[\bm r_1] = \bm F_0[\bm r_2]$ ¡ÊÎϤϤ½¤ÎºîÍÑÀþ¾å¤ò°ÜÆ°¤·¤Æ¤âƯ¤¤ÏÊѤï¤é¤Ê¤¤¡Ë
¤È¤¤¤¦À¼Á¤¬Æ³¤«¤ì¤Þ¤¹ [*]_ ¡¥
.. [*] $(\bm r - \bm r_1) \times \bm F_0$ ¤È¤Ê¤ëÅÀ $\bm r$ ¤Î½¸¹ç¤òÎÏ
$\bm F_0[\bm r_1]$ ¤ÎºîÍÑÀþ¤È¤¤¤¤¤Þ¤¹¡¥
Æó¤Ä¤ÎÎϤιçÎÏ
==============
Í¿¤¨¤é¤ì¤¿ $\bm F_1[\bm r_1]$, $\bm F_2[\bm r_2]$ ¤ËÂФ·¤Æ
<tex>
\bm F_1[\bm r_1] + \bm F_2[\bm r_2] = \bm F_3[\bm r_3]
</tex>
¤È¤Ê¤ë $\bm F_3[\bm r_3]$ ¤¬Â¸ºß¤¹¤ë¤È¤¡¤ $\bm F_3[\bm r_3]$ ¤ò $\bm F_1[\bm r_1]$,
$\bm F_2[\bm r_2]$ ¤Î¹çÎϤȤ¤¤¤¤Þ¤¹¡¥ $\bm F_1[\bm r_1]$, $\bm F_2[\bm r_2]$ ¤¬
Ʊ°ìÊ¿Ì̾å¤Ë¤¢¤ì¤Ð¡¤ $\bm F_1 + \bm F_2 = \bm 0$, $\bm r_1 \neq \bm r_2$
¤Î¾ì¹ç¤ò½ü¤¤¤Æ¡¤¹çÎϤ¬Â¸ºß¤·¤Þ¤¹¡¥
Ê¿¹Ô¤Ç¤Ê¤¤£²ÎÏ
--------------
$\bm F_1[\bm r_1]$, $\bm F_2[\bm r_2]$ ¤¬Ê¿¹Ô¤Ç¤Ê¤¤¤È¤¤Ï¡¤¤³¤ì¤é¤Î¥Ù¥¯¥È¥ë¤Ï
£±¼¡ÆÈΩ¤Ç¤¹¤«¤é $\bm r_1 - \bm r_2 = a \bm F_1 - b \bm F_2$ ¤È¤Ê¤ë $a$, $b$ ¤¬
¸ºß¤·¡¤
<tex>
\bm F_3 = \bm F_1 + \bm F_2
</tex>
<tex>
\bm r_3 = \bm r_1 - a \bm F_1 = \bm r_2 - b \bm F_2
</tex>
¤Èɽ¤»¤Þ¤¹¡Ê $\bm r_3$ ¤Ï£²ÎϤκîÍÑÀþ¤Î¸òÅÀ¡Ë¡¥
Î㤨¤Ð $\bm F_1[\bm r_1] = (F, 0)[(2r, 0)]$, $\bm F_2[\bm r_2] = (0, F)[(0, 2r)]$
¤Î¤È¤¡¤
<tex>
\left( \begin{array}{cc} 2r & -2r \\ \end{array} \right)
= \left( \begin{array}{cc} a & -b \\ \end{array} \right)
\left(\begin{array}{cc} F & 0 \\ 0 & F \\ \end{array} \right)
</tex>
¤Ç¤¹¤«¤é¡¤ $\bm F_3[\bm r_3] = (F, F)[(0, 0)]$ ¤È¤Ê¤ê¤Þ¤¹¡¥¤¿¤À¤·¡¤ $(0, 0)$ ¤Ï
¹äÂξå¤Ë¤Ê¤¤¤Î¤Ç¡¤ $\bm F_3[\bm r_3]$ ¤ÎºîÍÑÀþ¾å¤Ë¤¢¤ë¹äÂξå¤ÎÅÀ $\bm r_4=(r, r)$
¤òµá¤á¡¤ $\bm F_3[\bm r_3]$ ¤ÈÅù²Á¤Ê $\bm F_3[\bm r_4] = (F, F)[(r, r)]$ ¤ò
¹çÎϤȤ¹¤ëÊý¤¬¼«Á³¤Ç¤·¤ç¤¦ [*]_ ¡¥
.. figure:: pulsar-BoundVector-Fig2.gif
$(F, 0)[(2r, 0)] + (0, F)[(0, 2r)]$
.. [*] Ǥ°Õ¤Î $r_a$, $r_b$, $r_c$ ¤Ë¤Ä¤¤¤Æ
$(F, F)[(0, 0)] = (F, 0)[(r_a, r_b)] + (0, F)[(r_c, r_a)]$
¤¬À®Î©¤·¤Þ¤¹¡¥
Ê¿¹Ô¤Ê£²ÎÏ
----------
$\bm F_2 = c \bm F_1 \hspace{1zw} (c \neq -1)$ ¤Ç¤¢¤ì¤Ð¡¤
<tex>
\bm r_1 \times \bm F_1 + \bm r_2 \times \bm F_2
= (\bm r_1 + c \bm r_2) \times \bm F_1
</tex>
¤Ç¤¹¤«¤é¡¤
<tex>
\bm F_3 = (1 + c)\bm F_1
</tex>
<tex>
\bm r_3 = \frac{\bm r_1 + c \bm r_2}{1 + c}
</tex>
¤Ç¤¹¡¥
Î㤨¤Ð $\bm F_1[\bm r_1] = (0, -F)[(0, 0)]$,
$\bm F_2[\bm r_2] = (0, -2F)[(3r, 0)]$ ¤Î¤È¤¡¤
<tex>
\bm r_3 = \frac{(0, 0)+2(3r, 0)}{1+2} = (2r, 0)
</tex>
¤Ç¡¤ $\bm F_3[\bm r_3] = (0, -3F)[(2r, 0)]$ ¤È¤Ê¤ê¤Þ¤¹¡¥
.. figure:: pulsar-BoundVector-Fig3.gif
$(0, -F)[(0, 0)] + (0, -2F)[(3r, 0)]$
¶öÎÏ
====
$\bm F_1 + \bm F_2 = \bm 0$, $\bm r_1 \neq \bm r_2$ ¤Î¤È¤¡¤ $\bm F_1[\bm r_1]$,
$\bm F_2[\bm r_2]$ ¤Î¹çÎϤϸºß¤·¤Þ¤»¤ó¡¥¤³¤Î¤è¤¦¤ÊÎϤÎÁÈ $\bm F_1[\bm r_1]$,
$\bm F_2[\bm r_2]$ ¤ò¶öÎϤȤ¤¤¤¡¤°Ê²¼¤Ç¤Ï $\bm F_0[\bm r_1] - \bm F_0[\bm r_2]$
¤ò $\bm F_0[\bm r_1, \bm r_2]$ ¤Èάµ¤·¤Þ¤¹¡¥
¶öÎϤΥ⡼¥á¥ó¥È¤¬¼«Í³¥Ù¥¯¥È¥ë¤Ç¤¢¤ë¤³¤È¡¤¤¹¤Ê¤ï¤ÁǤ°Õ¤Î $\bm r_0$ ¤Ë¤Ä¤¤¤Æ
<tex>
\bm r_1 \times \bm F_0 + \bm r_2 \times (-\bm F_0)
= (\bm r_1 - \bm r_0) \times \bm F_0 + (\bm r_1 - \bm r_0) \times (-\bm F_0)
</tex>
¤¬À®Î©¤¹¤ë¤³¤È¤ä¡¤¶öÎÏ $\bm F_0[\bm r_1, \bm r_2]$ ¤È
¶öÎÏ $c^{-1} \bm F_0[c(\bm r_1 - \bm r_2), \bm 0]$ ¤Î¥â¡¼¥á¥ó¥È¤¬Åù¤·¤¤¤³¤ÈÅù¤¬
Íưפ˳Τ«¤á¤é¤ì¤Þ¤¹¡¥
£³¼¡¸µ¤ÎÎϤÎÅù²ÁÊÑ´¹
====================
$\bm F_1[\bm r_1]$, $\bm F_2[\bm r_2]$ ¤¬Æ±°ìÊ¿Ì̾å¤Ë¤Ê¤±¤ì¤Ð
¤³¤ì¤é¤Î¹çÎϤϸºß¤·¤Þ¤»¤ó¤¬¡¤Ç¤°Õ¤Î $\bm r_0$ ¤Ë¤Ä¤¤¤Æ
<tex>
\bm F_1[\bm r_1] + \bm F_2[\bm r_2]
= \bm F_3[\bm r_0] + \bm F_4[\bm r_4, \bm r_0]
</tex>
¤¬À®Î©¤¹¤ë¤è¤¦¤Ë $\bm F_3$, $\bm F_4$, $\bm r_4$ ¤òÁª¤Ö¤³¤È¤¬¤Ç¤¤Þ¤¹¡¥
.. figure:: pulsar-BoundVector-Fig4.gif
$\bm F_i[\bm r_i]$ ¤ÎÅù²ÁÊÑ´¹
Î㤨¤Ð¡¤ $\bm F_i[\bm r_i]$ ¤ò
<tex>
\bm F_i[\bm r_i]
= \bm F_i[\bm r_0] + \bm F_i[\bm r_i] - \bm F_i[\bm r_0]
= \bm F_i[\bm r_0] + \bm F_i[\bm r_i, \bm r_0]
</tex>
¤ÈÊÑ·Á¤·¤Æ²Ã»»¤·¤¿¼°
<tex>
\sum_{i=1}^2 \bm F_i[\bm r_i]
= \left( \sum_{i=1}^2 \bm F_i \right)[\bm r_0] + \sum_{i=1}^2 \bm F_i[\bm r_i, \bm r_0]
</tex>
¤Î±¦ÊÕÂ裲¹à¤Ï¶öÎϤÎϤǤ¹¤«¤é¡¤¼«Í³¥Ù¥¯¥È¥ë¤Ç¤¢¤ë¤³¤ì¤é¤Î¥â¡¼¥á¥ó¥È¤ÎÏÂ
<tex>
\bm N = \sum_{i=1}^2 (\bm r_i - \bm r_0) \times \bm F_i
</tex>
¤ÏÍưפ˷׻»¤Ç¤¡¤ $(\bm r_4 - \bm r_0) \times \bm F_4 = \bm N$ ¤òËþ¤¹¤ë $\bm F_4$,
$\bm r_4$ ¤¬µá¤á¤é¤ì¤Þ¤¹ [*]_ ¡¥
.. [*] $\bm N$ ¤¬ $\bm F_3$ ¤ÈÊ¿¹Ô¤Ç¤Ê¤¤¤È¤¡¤ $\bm F_3$ ¤ÈÊ¿¹Ô¤Ê¶öÎϤÎÀ®Ê¬¤ò
$\bm F_3$ ¤Ë²Ã»»¤·¡Ê¹çÎϤ¬Â¸ºß¤·¤Þ¤¹¡Ë¡¤¤³¤ì¤È $\bm F_3$ ¤Èľ¸ò¤¹¤ë¶öÎÏ
¡Ê¥â¡¼¥á¥ó¥È¤Ï $\bm F_3$ ¤ÈÊ¿¹Ô¡Ë¤È¤ÎϤËÊÑ·Á¤Ç¤¤Þ¤¹¡¥
¾å¼°¤Ç $\bm r_0$ ¤¬Ç¤°Õ¤ÎÅÀ¤Ç¤è¤«¤Ã¤¿¤³¤È¤ò»×¤¤½Ð¤¹¤È¡¤Â¿¿ô¤Î£³¼¡¸µ¥Ù¥¯¥È¥ë
$\bm F_1[\bm r_1], \cdots , \bm F_n[\bm r_n]$ ¤Ë¤Ä¤¤¤Æ¤â
<tex>
\sum_{i=1}^n \bm F_i[\bm r_i]
= \bm F_{n+1}[\bm r_0] + \bm F_{n+2}[\bm r_{n+2}, \bm r_0]
</tex>
¤È¤Ê¤ë $\bm F_{n+1}$, $\bm F_{n+2}$, $\bm r_{n+2}$ ¤¬Â¸ºß¤¹¤ë¤³¤È¤¬Ê¬¤«¤ê¤Þ¤¹¡¥
°ìÍͤÊÌ©Å٤ιäÂΤËƯ¤¯ÎÏ
========================
½ÅÎÏ
----
$\bm F_0[\bm r_0 - \bm r_1] + \bm F_0[\bm r_0 + \bm r_2] = 2 \bm F_0[\bm r_0]$
¤Ç¤¹¤«¤é¡¤Ì©ÅÙ¤¬°ìÍͤǡ¤ÅÀ $\bm r_0$ ¤Ë´Ø¤·¤ÆÂоΤʹäÂΤËƯ¤¯½ÅÎϤϡ¤½Å¿´¤ò
ºîÍÑÅÀ¤È¤·¡¤Â礤µ¤È¸þ¤¤¬ÎϤÎÁíϤËÅù¤·¤¤ÎϤÈÅù²Á¤Ç¤¢¤ë¤³¤È¤¬Ê¬¤«¤ê¤Þ¤¹¡¥
Î㤨¤Ð¡¤Î¾Ã¼¤¬ $\bm r_1$, $\bm r_2$ ¤Ë¤¢¤ë¼ÁÎÌ $M$ ¤ÎËÀ¤ËƯ¤¯½ÅÎϤϡ¤ËÀ¤ò $2 n$
¸Ä¤ÎÈù¾®Îΰè¤ËÅùʬ¤·¤ÆÅÀÂоΤʰÌÃ֤ˤ¢¤ëÈù¾®Îΰè¤ÎÂФò¹Í¤¨¤ë¤È¡¤³ÆÂФιçÎϤÎ
ºîÍÑÅÀ¤Ï¤¹¤Ù¤ÆËÀ¤ÎÃæ¿´¤Ë¤Ê¤ê¡¤¤³¤ì¤é¤Î¹çÎϤÎÁíϤ¬ËÀ¤ËƯ¤¯½ÅÎϤÈÅù¤·¤¯¤Ê¤ê¤Þ¤¹¡¥
¸ÇÄêÅÀ¤«¤é¼õ¤±¤ëÎÏ
------------------
¹äÂΤ¬¸ÇÄêÅÀ¤Î²ó¤ê¤ò±¿Æ°¤·¤Æ¤¤¤ë¤È¤¡¤Ä̾ï¤Ï¸ÇÄêÅÀ²ó¤ê¤Î³Ñ±¿Æ°Î̤λþ´ÖÈùʬ¤¬
¸ÇÄêÅÀ²ó¤ê¤Î³°ÎϤΥ⡼¥á¥ó¥È¤ÎÁíϤËÅù¤·¤¤¤È¤·¤Æ±¿Æ°ÊýÄø¼°¤ò²ò¤¤Þ¤¹¡¥¤³¤Î¾ì¹ç¡¤
¸ÇÄêÅÀ¤ËƯ¤¤¤Æ¤¤¤ëÎϤò·×»»¤¹¤ëɬÍפϤ¢¤ê¤Þ¤»¤ó¤¬¡¤¾åµ¤ÎÀâÌÀ¤È´ØÏ¢ÉÕ¤±¤ë¤¿¤á¤Ë
¸ÇÄêÅÀ $\bm r_0$ ¤ËƯ¤¯ÎϤ¬ $\bm F_0[\bm r_0]$, ¤½¤Î¾¤Î³°ÎϡʽÅÎϤϽſ´¤Ë½¸Ãæ
¤·¤Æ¤¤¤ë¤È¤·¤Æ°·¤¤¤Þ¤¹¡Ë¤¬ $\bm F_i[\bm r_i]$ $(i = 1, \cdots , n)$ ¤Ç¤¢¤ë¾ì¹ç
¤Ë¤Ä¤¤¤Æ¹Í¤¨¤Þ¤·¤ç¤¦¡¥
¤³¤Î¹äÂΤËƯ¤¯ÎϤÏ
<tex>
\bm F[\bm r] = \left( \sum_{i=0}^n \bm F_i \right) [\bm r]
+ \sum_{i=0}^n \bm F_i[\bm r_i, \bm r]
</tex>
¤ÈÅù²Á¤Ç¤¹¤«¤é¡¤ $\bm r = \bm r_0$ ¤È¤ª¤¯¤È $\bm r_0$ ²ó¤ê¤Î³Ñ±¿Æ°Î̤òµá¤á¤ë
ÊýÄø¼°¤«¤é $\bm F_0$ ¤¬¾Ã¤¨¤Æ¤·¤Þ¤¤¤Þ¤¹¡¥¤Ä¤Þ¤ê¡¤ $\bm F_0$ ¤òµá¤á¤ëɬÍפ¬¤Ê¤±¤ì¤Ð
±¿Æ°Î̤òµá¤á¤ëÊýÄø¼°¤Ï¹Í¤¨¤Ê¤¯¤Æ¤è¤¤¤Î¤Ç¤¹¡¥
¿ôÃÍÎã¤Ë¤Ä¤¤¤Æ
==============
¡ÖÆó¤Ä¤ÎÎϤιçÎϡפǤϡ¤¿ôÃÍÎã¤Ë $\bm F_1[\bm r_1] = (0, -F)[(0, 0)]$,
$\bm F_2[\bm r_2] = (0, -2F)[(3r, 0)]$ ¤Î¤è¤¦¤Êɽ¸½¤òÍѤ¤¤Þ¤·¤¿¡¥¤³¤ÎÅÀ¤Ë¤Ä¤¤¤Æ
Ê䤷¤Þ¤¹¡¥
Ä̾ʪÍýÎ̤òɽ¤¹Ê¸»ú¤Ïñ°Ì¤ò´Þ¤ó¤Ç¤¤¤Þ¤¹¡¥Î㤨¤Ð¡¤Â®¤µ $v$ ¤Ç»þ´Ö $t$ ¤À¤±
°ÜÆ°¤·¤¿¤È¤¤Î°ÜÆ°µ÷Î¥¤Ï $vt$ ¤Ç¤¢¤ë¤È¤¤¤Ã¤¿¤È¤¡¤ $v$ ¤ä $t$ ¤Îñ°Ì¤Ï¼«Í³¤ËÁª¤Ù¤Þ¤¹¡¥
$v = 72 \mathrm{km/h}$, $t = 3 \mathrm{s}$ ¤Ê¤é¤Ð $vt = 60 \mathrm{m}$ ¤Ç¤¹¡¥
¤Ê¤ª¡¤Â®¤µ $v$ ¤Ç $1 \mathrm{s}$ ´Ö°ÜÆ°¤·¤¿¤È¤¤Î°ÜÆ°µ÷Î¥¤Ï $v$ ¤Ç¤Ï¤Ê¤¯
$(1 \mathrm{s})v$ ¤Ç¤¹ [*]_ ¡¥¾åµ¤Î $(0, -2F)[(3r, 0)]$ ¤Î¤è¤¦¤Ê¿ôÃÍÎã¤Ï
$(0, -2 \mathrm{N})[(3 \mathrm{m}, 0)]$ ¤Î¤è¤¦¤Êɽ¸½¤è¤êʬ¤«¤ê¤ä¤¹¤¤¤È»×¤¤¤Þ¤¹¡¥
.. [*] $0 \mathrm{km/h} = 0 \mathrm{m/s}$ ¤À¤«¤é $v = 0$ ¤Î±¦ÊÕ¤Ëñ°Ì¤ÏÉÔÍפǤ¹¤¬¡¤
²¹ÅÙ $T = 0^{\circ} \mathrm C$ ¤Îñ°Ì¤Ï¾Êά¤Ç¤¤Þ¤»¤ó¡¥
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