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3¾Ï¤Î±é½¬ÌäÂê

  1. (Cauchy ¤Î´Ø·¸)

    (a) ¿Þ1¤ÎÍͤˡ¤ÅÀP¤Ë¤ª¤±¤ëË¡Àþ¥Ù¥¯¥È¥ë¤¬¤½¤ì¤¾¤ì¡¤ \(\mbox{\boldmath$n$}\)¡¤ \(\mbox{\boldmath$n$}^\prime\) ¤Ç¤¢¤ëÌÌÀÑÍ×ÁÇ\(d S\)¤È\(d S^\prime\)¤ò¹Í¤¨¤ë¡¥¼¡¤Î¼°¤¬À®¤êΩ¤Ä¤³¤È¤ò¾ÚÌÀ¤·¤Ê¤µ¤¤¡¥


    \begin{displaymath} \stackrel{n^\prime}{\mbox{\boldmath$T$}}\cdot \mbox{\boldmat... ...ackrel{n}{\mbox{\boldmath$T$}}\cdot \mbox{\boldmath$n$}^\prime \end{displaymath} (166)

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    ¿Þ1

    (b) Ë¡Àþ±þÎϤ¬ÄäαÃÍ(¶ËÂç¤Þ¤¿¤Ï¶Ë¾®ÃÍ)¤ò»ý¤Ä»þ¤Î¤»¤óÃDZþÎÏ ¤ÏÎí¤Ç¤¢¤ë¤³¤È¤ò¼¨¤·¤Ê¤µ¤¤¡¥
    \(\left( \begin{minipage}{14cm} ¥Ò¥ó¥È:¿Þ2¤Î¤è¤¦¤Ë¡¤ Ë¡Àþ¥Ù¥¯¥È¥ë¤¬\(\mbox{\bold... ..., \cos d\theta \approx 1\)¤È¶á»÷¤·¡¤¹â¼¡¤Î¹à¤ò̵»ë¤¹¤ë¡¥ \end{minipage}\right)\)

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  2. (¼ç±þÎÏ)

    ¼ç±þÎϤòµá¤á¤ë¤¿¤á¤Î ÆÃÀ­ÊýÄø¼° \({\rm det}(\sigma_{ij}-\sigma\delta_{ij})=0\)¤Ï¡¤ 3¤Ä¤Î¼Â¿ô²ò¤ò»ý¤Ä¤³¤È¤ò¼¨¤·¤Ê¤µ¤¤¡¥
    \(\left( \begin{minipage}{14cm} ¥Ò¥ó¥È: 3¼¡ÊýÄø¼°¤Î²ò¤Î¤¦¤Á¾¯¤Ê¤¯¤È¤â¤Ò¤È¤Ä¤Ï¼Â¿... ...1, \sigma_2\)¤òµá¤á¤ë2¼¡ÊýÄø¼°¤Ë¤ª¤±¤ëȽÊ̼°¤òɾ²Á¤¹¤ë¡¥ \end{minipage}\right)\)

  3. (±þÎϤÎÉÔÊÑÎÌ)

    (a) ºÂɸÊÑ´¹¤ÎÊý¸þ;¸¹\(Q_{ij}\)¤ËÂФ·¤Æ¡¤

    \begin{displaymath} Q_{ki}Q_{kj}=\delta_{ij}, \qquad Q_{ik}Q_{jk}=\delta_{ij}, \qquad {\rm det}(Q_{ij})=1 \end{displaymath} (167)

    ¤ò¼¨¤·¤Ê¤µ¤¤¡¥

    (b) ¾å¤Î´Ø·¸¤òÍøÍѤ·¤Æ¡¤

    \begin{displaymath} \begin{array}{l} J_1 = \sigma_{ii}, \qquad J_2 = \displaysty... ...ip}\sigma_{jq}\sigma_{kr} = {\rm det}(\sigma_{ij}) \end{array}\end{displaymath} (168)

    ¤¬¡¤ÉÔÊÑÎÌ (¤Ä¤Þ¤ê¡¤Ç¤°Õ¤ÎºÂɸÊÑ´¹\(Q_{ij}\)¤ÇÊÑ´¹¤·¤Æ¤âÊÑ´¹¤ÎÁ°¸å¤ÇÃͤ¬ÊѤï¤é¤Ê¤¤ÎÌ) ¤Ç¤¢¤ë¤³¤È¤ò¾ÚÌÀ¤·¤Ê¤µ¤¤¡¥

  4. (¶ËºÂɸ·Ï¤Ë¤ª¤±¤ë¤Ä¤ê¤¢¤¤ÊýÄø¼°)

    ±ßÃìºÂɸ¤Ë¤ª¤±¤ë¤Ä¤ê¤¢¤¤ÊýÄø¼° (±þÎÏÀ®Ê¬¡¤ \(\sigma_{rr}, \sigma_{r\theta}, \sigma_{rz}, \cdots, \sigma_{zz}\) ¤ò´Ø·¸¤Å¤±¤ë¼°) ¤ò¼¡¤ÎÆóÄ̤ê¤ÎÊýË¡¤Ë¤è¤êƳ¤­¤Ê¤µ¤¤¡¥

    (a) ¿Þ3¤ÎÍͤÊÈù¾®Àð·ÁÍ×ÁǤΤĤꤢ¤¤¤ò¹Í¤¨¤ë¡¥

    (b) ľ³ÑºÂɸ¤Ë¤ª¤±¤ë¤Ä¤ê¤¢¤¤ÊýÄø¼°¤òºÂɸÊÑ´¹¤¹¤ë¡¥

    (;ÎϤΤ¢¤ë¿Í¤Ï¡¤µåºÂɸ·Ï¤Î¤Ä¤ê¤¢¤¤ÊýÄø¼°(±þÎÏÀ®Ê¬¡¤ \(\sigma_{rr}, \sigma_{r\theta}, \sigma_{r\phi}, \cdots, \sigma_{\phi\phi}\)¤ò´Ø·¸¤Å¤±¤ë¼°)¤Ë¤Ä¤¤¤Æ¤âƳ¤­¤Ê¤µ¤¤(¿Þ4)¡¥

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Akihiro Nakatani 2001-06-25