{"id":19755,"date":"2025-05-10T12:59:27","date_gmt":"2025-05-10T03:59:27","guid":{"rendered":"https:\/\/123210.net\/wordpress\/tatenaoshi\/?p=19755"},"modified":"2025-05-10T12:59:27","modified_gmt":"2025-05-10T03:59:27","slug":"%e5%9c%b0%e9%9c%87%e6%b3%a2%e3%81%a8%e3%83%9b%e3%83%83%e3%82%b8%e5%88%86%e8%a7%a3%e3%81%ae%e9%96%a2%e4%bf%82%e3%82%92%e6%95%99%e3%81%88%e3%81%a6%e3%81%8f%e3%81%a0%e3%81%95%e3%81%84","status":"publish","type":"post","link":"https:\/\/123210.net\/wordpress\/tatenaoshi\/%e5%9c%b0%e9%9c%87%e6%b3%a2%e3%81%a8%e3%83%9b%e3%83%83%e3%82%b8%e5%88%86%e8%a7%a3%e3%81%ae%e9%96%a2%e4%bf%82%e3%82%92%e6%95%99%e3%81%88%e3%81%a6%e3%81%8f%e3%81%a0%e3%81%95%e3%81%84\/","title":{"rendered":"\u5730\u9707\u6ce2\u3068\u30db\u30c3\u30b8\u5206\u89e3\u306e\u95a2\u4fc2\u3092\u6559\u3048\u3066\u304f\u3060\u3055\u3044"},"content":{"rendered":"
\n
\u5730\u9707\u6ce2\u3068\u30db\u30c3\u30b8\u5206\u89e3\u306e\u95a2\u4fc2\u306f\u3001\u5730\u9707\u5b66\u306b\u304a\u3051\u308b\u6ce2\u52d5\u5834\u306e\u89e3\u6790\u3084\u30e2\u30c7\u30ea\u30f3\u30b0\u306b\u304a\u3044\u3066\u3001\u30d9\u30af\u30c8\u30eb\u5834\u3084\u30c6\u30f3\u30bd\u30eb\u5834\u3092\u7269\u7406\u7684\u306b\u610f\u5473\u306e\u3042\u308b\u6210\u5206\u306b\u5206\u89e3\u3059\u308b\u969b\u306b\u73fe\u308c\u307e\u3059\u3002\u30db\u30c3\u30b8\u5206\u89e3\uff08\u307e\u305f\u306f\u305d\u306e\u7279\u5225\u306a\u5834\u5408\u3067\u3042\u308b\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u5206\u89e3\uff09\u306f\u3001\u5730\u9707\u6ce2\u306e\u901f\u5ea6\u5834\u3084\u5909\u4f4d\u5834\u3092\u300c\u767a\u6563\u6210\u5206\u300d\uff08\u5727\u7e2e\u6ce2\uff1aP\u6ce2\uff09\u3068\u300c\u56de\u8ee2\u6210\u5206\u300d\uff08\u305b\u3093\u65ad\u6ce2\uff1aS\u6ce2\uff09\u306b\u5206\u96e2\u3059\u308b\u5f37\u529b\u306a\u6570\u5b66\u7684\u30c4\u30fc\u30eb\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001\u5730\u9707\u6ce2\u3068\u30db\u30c3\u30b8\u5206\u89e3\u306e\u95a2\u4fc2\u3092\u3001\u5730\u9707\u5b66\u306e\u6587\u8108\u3001\u6570\u5b66\u7684\u67a0\u7d44\u307f\u3001\u5177\u4f53\u4f8b\u3001\u5fdc\u7528\u3092\u901a\u3058\u3066\u8a73\u7d30\u306b\u89e3\u8aac\u3057\u307e\u3059\u3002<\/span><\/span><\/div>\n
\n
1. \u5730\u9707\u6ce2\u306e\u6982\u8981<\/span><\/span><\/div>\n
\u5730\u9707\u6ce2\u306f\u3001\u5730\u7403\u5185\u90e8\u3084\u8868\u9762\u3092\u4f1d\u64ad\u3059\u308b\u5f3e\u6027\u6ce2\u3067\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e\u7a2e\u985e\u306b\u5206\u985e\u3055\u308c\u307e\u3059\uff1a<\/span><\/span><\/div>\n
    \n
  • \n
    P\u6ce2\uff08\u5727\u7e2e\u6ce2\u3001Primary wave\uff09<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
      \n
    • \n
      \u7e26\u6ce2\u3067\u3001\u5a92\u8cea\u3092\u5727\u7e2e\u30fb\u81a8\u5f35\u3055\u305b\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n
    • \n
      \u767a\u6563\u6210\u5206\uff08<\/span><\/span><\/p>\n
      \u2207\u22c5u\u22600\\nabla \\cdot \\mathbf{u} \\neq 0<\/span>\\nabla \\cdot \\mathbf{u} \\neq 0<\/code><\/div>\n

      \uff09\u3092\u6301\u3061\u3001\u56de\u8ee2\u6210\u5206\u306f\u30bc\u30ed\uff08<\/span><\/span><\/p>\n

      \u2207\u00d7u=0\\nabla \\times \\mathbf{u} = 0<\/span>\\nabla \\times \\mathbf{u} = 0<\/code><\/div>\n

      \uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

    • \n
      \u4f1d\u64ad\u901f\u5ea6\u304c\u901f\u304f\u3001\u6700\u521d\u306b\u89b3\u6e2c\u3055\u308c\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n
    • \n
      S\u6ce2\uff08\u305b\u3093\u65ad\u6ce2\u3001Secondary wave\uff09<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
        \n
      • \n
        \u6a2a\u6ce2\u3067\u3001\u5a92\u8cea\u3092\u305b\u3093\u65ad\u5909\u5f62\u3055\u305b\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n
      • \n
        \u56de\u8ee2\u6210\u5206\uff08<\/span><\/span><\/p>\n
        \u2207\u00d7u\u22600\\nabla \\times \\mathbf{u} \\neq 0<\/span>\\nabla \\times \\mathbf{u} \\neq 0<\/code><\/div>\n

        \uff09\u3092\u6301\u3061\u3001\u767a\u6563\u6210\u5206\u306f\u30bc\u30ed\uff08<\/span><\/span><\/p>\n

        \u2207\u22c5u=0\\nabla \\cdot \\mathbf{u} = 0<\/span>\\nabla \\cdot \\mathbf{u} = 0<\/code><\/div>\n

        \uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

      • \n
        P\u6ce2\u3088\u308a\u9045\u3044\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n
      • \n
        \u8868\u9762\u6ce2\uff08Love\u6ce2\u3001Rayleigh\u6ce2\uff09<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
          \n
        • \n
          \u5730\u7403\u8868\u9762\u306b\u6cbf\u3063\u3066\u4f1d\u64ad\u3002<\/span><\/span><\/div>\n<\/li>\n
        • \n
          \u8907\u96d1\u306a\u5909\u4f4d\u30d1\u30bf\u30fc\u30f3\u3092\u6301\u3061\u3001P\u6ce2\u30fbS\u6ce2\u306e\u6210\u5206\u304c\u6df7\u5728\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n
          \u5730\u9707\u6ce2\u306e\u5909\u4f4d\u5834 <\/span><\/span><\/p>\n
          u(x,t)\\mathbf{u}(\\mathbf{x}, t)<\/span>\\mathbf{u}(\\mathbf{x}, t)<\/code><\/div>\n

          \u3084\u901f\u5ea6\u5834 <\/span><\/span><\/p>\n

          v=\u2202tu\\mathbf{v} = \\partial_t \\mathbf{u}<\/span>\\mathbf{v} = \\partial_t \\mathbf{u}<\/code><\/div>\n

          \u306f\u30d9\u30af\u30c8\u30eb\u5834\u3067\u3042\u308a\u3001\u30db\u30c3\u30b8\u5206\u89e3\u3092\u7528\u3044\u3066\u3053\u308c\u3089\u306e\u5834\u3092P\u6ce2\u3068S\u6ce2\u306b\u5bfe\u5fdc\u3059\u308b\u6210\u5206\u306b\u5206\u96e2\u3067\u304d\u307e\u3059\u3002<\/span><\/span><\/div>\n

          \n
          2. \u30db\u30c3\u30b8\u5206\u89e3\u3068\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u5206\u89e3<\/span><\/span><\/div>\n
          \u30db\u30c3\u30b8\u5206\u89e3\u306f\u3001\u30d9\u30af\u30c8\u30eb\u5834\u3092\u6b21\u306e\u3088\u3046\u306b\u5206\u89e3\u3057\u307e\u3059\uff1a <\/span><\/span><\/p>\n
          F=\u2207\u03d5+\u2207\u00d7A+H,\\mathbf{F} = \\nabla \\phi + \\nabla \\times \\mathbf{A} + \\mathbf{H},<\/span>\\mathbf{F} = \\nabla \\phi + \\nabla \\times \\mathbf{A} + \\mathbf{H},<\/code><\/div>\n<\/div>\n
            \n
          • \n
            \n
            \u2207\u03d5\\nabla \\phi<\/span>\\nabla \\phi<\/code><\/div>\n

            \uff1a\u52fe\u914d\u5834\uff08\u767a\u6563\u6210\u5206\u3001\u56de\u8ee2\u30bc\u30ed\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

          • \n
            \n
            \u2207\u00d7A\\nabla \\times \\mathbf{A}<\/span>\\nabla \\times \\mathbf{A}<\/code><\/div>\n

            \uff1a\u56de\u8ee2\u5834\uff08\u767a\u6563\u30bc\u30ed\u3001\u56de\u8ee2\u6210\u5206\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

          • \n
            \n
            H\\mathbf{H}<\/span>\\mathbf{H}<\/code><\/div>\n

            \uff1a\u8abf\u548c\u5834\uff08<\/span><\/span><\/p>\n

            \u2207\u22c5H=0,\u2207\u00d7H=0\\nabla \\cdot \\mathbf{H} = 0, \\nabla \\times \\mathbf{H} = 0<\/span>\\nabla \\cdot \\mathbf{H} = 0, \\nabla \\times \\mathbf{H} = 0<\/code><\/div>\n

            \uff09\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n

            \u5730\u9707\u5b66\u3067\u306f\u3001\u5730\u7403\u5185\u90e8\uff08\u975e\u30b3\u30f3\u30d1\u30af\u30c8\u306a <\/span><\/span><\/p>\n
            R3\\mathbb{R}^3<\/span>\\mathbb{R}^3<\/code><\/div>\n

            \uff09\u3092\u6271\u3046\u305f\u3081\u3001\u8abf\u548c\u6210\u5206 <\/span><\/span><\/p>\n

            H\\mathbf{H}<\/span>\\mathbf{H}<\/code><\/div>\n

            \u306f\u901a\u5e38\u3001\u7121\u9650\u9060\u3067\u306e\u6e1b\u8870\u6761\u4ef6\u306b\u3088\u308a\u30bc\u30ed\u3068\u4eee\u5b9a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30db\u30c3\u30b8\u5206\u89e3\u306f\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u5206\u89e3\u306b\u7c21\u7565\u5316\uff1a <\/span><\/span><\/p>\n

            u=\u2207\u03d5+\u2207\u00d7A,\\mathbf{u} = \\nabla \\phi + \\nabla \\times \\mathbf{A},<\/span>\\mathbf{u} = \\nabla \\phi + \\nabla \\times \\mathbf{A},<\/code><\/div>\n

            \u3053\u3053\u3067\uff1a<\/span><\/span><\/div>\n

              \n
            • \n
              \n
              \u03d5\\phi<\/span>\\phi<\/code><\/div>\n

              \uff1a\u30b9\u30ab\u30e9\u30fc\u5834\uff08P\u6ce2\u306b\u5bfe\u5fdc\u3059\u308b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

            • \n
              \n
              A\\mathbf{A}<\/span>\\mathbf{A}<\/code><\/div>\n

              \uff1a\u30d9\u30af\u30c8\u30eb\u5834\uff08S\u6ce2\u306b\u5bfe\u5fdc\u3059\u308b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3001<\/span><\/span><\/p>\n

              \u2207\u22c5A=0\\nabla \\cdot \\mathbf{A} = 0<\/span>\\nabla \\cdot \\mathbf{A} = 0<\/code><\/div>\n

              \u3092\u8ab2\u3059\u3053\u3068\u304c\u591a\u3044\uff1aCoulomb gauge\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n

              \u7269\u7406\u7684\u5bfe\u5fdc<\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                \n
              • \n
                \n
                \u2207\u03d5\\nabla \\phi<\/span>\\nabla \\phi<\/code><\/div>\n

                \uff1a\u767a\u6563\u6210\u5206\uff08<\/span><\/span><\/p>\n

                \u2207\u22c5u\u22600\\nabla \\cdot \\mathbf{u} \\neq 0<\/span>\\nabla \\cdot \\mathbf{u} \\neq 0<\/code><\/div>\n

                \uff09\u3067\u3001P\u6ce2\uff08\u5727\u7e2e\u30fb\u81a8\u5f35\uff09\u3092\u8a18\u8ff0\u3002<\/span><\/span><\/div>\n<\/li>\n

              • \n
                \n
                \u2207\u00d7A\\nabla \\times \\mathbf{A}<\/span>\\nabla \\times \\mathbf{A}<\/code><\/div>\n

                \uff1a\u56de\u8ee2\u6210\u5206\uff08<\/span><\/span><\/p>\n

                \u2207\u22c5u=0\\nabla \\cdot \\mathbf{u} = 0<\/span>\\nabla \\cdot \\mathbf{u} = 0<\/code><\/div>\n

                \uff09\u3067\u3001S\u6ce2\uff08\u305b\u3093\u65ad\uff09\u3092\u8a18\u8ff0\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n

                \n
                3. \u5730\u9707\u6ce2\u3078\u306e\u30db\u30c3\u30b8\u5206\u89e3\u306e\u9069\u7528<\/span><\/span><\/div>\n
                \u5730\u9707\u6ce2\u306e\u5909\u4f4d\u5834 <\/span><\/span><\/p>\n
                u(x,t)\\mathbf{u}(\\mathbf{x}, t)<\/span>\\mathbf{u}(\\mathbf{x}, t)<\/code><\/div>\n

                \u3092\u30db\u30c3\u30b8\u5206\u89e3\u3067\u89e3\u6790\u3059\u308b\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/span><\/span><\/div>\n

                (1) \u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/span><\/span><\/div>\n
                \u5730\u9707\u6ce2\u306f\u3001\u5f3e\u6027\u4f53\u306e\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306b\u5f93\u3044\u307e\u3059\uff1a <\/span><\/span><\/p>\n
                \u03c1\u2202t2u=(\u03bb+2\u03bc)\u2207(\u2207\u22c5u)\u2212\u03bc\u2207\u00d7(\u2207\u00d7u),\\rho \\partial_t^2 \\mathbf{u} = (\\lambda + 2\\mu) \\nabla (\\nabla \\cdot \\mathbf{u}) – \\mu \\nabla \\times (\\nabla \\times \\mathbf{u}),<\/span>\\rho \\partial_t^2 \\mathbf{u} = (\\lambda + 2\\mu) \\nabla (\\nabla \\cdot \\mathbf{u}) - \\mu \\nabla \\times (\\nabla \\times \\mathbf{u}),<\/code><\/div>\n<\/div>\n
                  \n
                • \n
                  \n
                  \u03c1\\rho<\/span>\\rho<\/code><\/div>\n

                  \uff1a\u5bc6\u5ea6\u3002<\/span><\/span><\/div>\n<\/li>\n

                • \n
                  \n
                  \u03bb,\u03bc\\lambda, \\mu<\/span>\\lambda, \\mu<\/code><\/div>\n

                  \uff1a\u30e9\u30e1\u5b9a\u6570\uff08\u5f3e\u6027\u4fc2\u6570\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                • \n
                  \n
                  \u2207\u22c5u\\nabla \\cdot \\mathbf{u}<\/span>\\nabla \\cdot \\mathbf{u}<\/code><\/div>\n

                  \uff1a\u767a\u6563\uff08P\u6ce2\u306e\u5bc4\u4e0e\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                • \n
                  \n
                  \u2207\u00d7u\\nabla \\times \\mathbf{u}<\/span>\\nabla \\times \\mathbf{u}<\/code><\/div>\n

                  \uff1a\u56de\u8ee2\uff08S\u6ce2\u306e\u5bc4\u4e0e\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n

                  \u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001P\u6ce2\u3068S\u6ce2\u304c\u7570\u306a\u308b\u901f\u5ea6\u3067\u4f1d\u64ad\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\uff1a<\/span><\/span><\/div>\n
                    \n
                  • \n
                    P\u6ce2\u901f\u5ea6\uff1a<\/span><\/span><\/p>\n
                    vP=(\u03bb+2\u03bc)\/\u03c1v_P = \\sqrt{(\\lambda + 2\\mu)\/\\rho}<\/span>v_P = \\sqrt{(\\lambda + 2\\mu)\/\\rho}<\/code><\/div>\n

                    \u3002<\/span><\/span><\/div>\n<\/li>\n

                  • \n
                    S\u6ce2\u901f\u5ea6\uff1a<\/span><\/span><\/p>\n
                    vS=\u03bc\/\u03c1v_S = \\sqrt{\\mu\/\\rho}<\/span>v_S = \\sqrt{\\mu\/\\rho}<\/code><\/div>\n

                    \uff08<\/span><\/span><\/p>\n

                    vS<vPv_S < v_P<\/span>v_S < v_P<\/code><\/div>\n

                    \uff09\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n

                    (2) \u30db\u30c3\u30b8\u5206\u89e3\u306e\u9069\u7528<\/span><\/span><\/div>\n
                    \u5909\u4f4d\u5834 <\/span><\/span><\/p>\n
                    u\\mathbf{u}<\/span>\\mathbf{u}<\/code><\/div>\n

                    \u3092\u6b21\u306e\u3088\u3046\u306b\u5206\u89e3\uff1a <\/span><\/span><\/p>\n

                    u=\u2207\u03d5+\u2207\u00d7A,\u2207\u22c5A=0.\\mathbf{u} = \\nabla \\phi + \\nabla \\times \\mathbf{A}, \\quad \\nabla \\cdot \\mathbf{A} = 0.<\/span>\\mathbf{u} = \\nabla \\phi + \\nabla \\times \\mathbf{A}, \\quad \\nabla \\cdot \\mathbf{A} = 0.<\/code><\/div>\n<\/div>\n
                      \n
                    • \n
                      P\u6ce2\u6210\u5206<\/span><\/span><\/span>\uff1a<\/span><\/span><\/p>\n
                      uP=\u2207\u03d5\\mathbf{u}_P = \\nabla \\phi<\/span>\\mathbf{u}_P = \\nabla \\phi<\/code><\/div>\n

                      \u3002\u3053\u3053\u3067\uff1a<\/span><\/span><\/div>\n

                        \n
                      • \n
                        \n
                        \u2207\u22c5uP=\u2207\u22c5(\u2207\u03d5)=\u0394\u03d5\\nabla \\cdot \\mathbf{u}_P = \\nabla \\cdot (\\nabla \\phi) = \\Delta \\phi<\/span>\\nabla \\cdot \\mathbf{u}_P = \\nabla \\cdot (\\nabla \\phi) = \\Delta \\phi<\/code><\/div>\n

                        \uff08\u767a\u6563\u975e\u30bc\u30ed\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                      • \n
                        \n
                        \u2207\u00d7uP=\u2207\u00d7(\u2207\u03d5)=0\\nabla \\times \\mathbf{u}_P = \\nabla \\times (\\nabla \\phi) = 0<\/span>\\nabla \\times \\mathbf{u}_P = \\nabla \\times (\\nabla \\phi) = 0<\/code><\/div>\n

                        \uff08\u56de\u8ee2\u30bc\u30ed\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                      • \n
                        \n
                        \u03d5\\phi<\/span>\\phi<\/code><\/div>\n

                        \u306f\u6ce2\u52d5\u65b9\u7a0b\u5f0f <\/span><\/span><\/p>\n

                        \u2202t2\u03d5=vP2\u0394\u03d5\\partial_t^2 \\phi = v_P^2 \\Delta \\phi<\/span>\\partial_t^2 \\phi = v_P^2 \\Delta \\phi<\/code><\/div>\n

                        \u3092\u6e80\u305f\u3059\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n

                      • \n
                        S\u6ce2\u6210\u5206<\/span><\/span><\/span>\uff1a<\/span><\/span><\/p>\n
                        uS=\u2207\u00d7A\\mathbf{u}_S = \\nabla \\times \\mathbf{A}<\/span>\\mathbf{u}_S = \\nabla \\times \\mathbf{A}<\/code><\/div>\n

                        \u3002\u3053\u3053\u3067\uff1a<\/span><\/span><\/div>\n

                          \n
                        • \n
                          \n
                          \u2207\u22c5uS=\u2207\u22c5(\u2207\u00d7A)=0\\nabla \\cdot \\mathbf{u}_S = \\nabla \\cdot (\\nabla \\times \\mathbf{A}) = 0<\/span>\\nabla \\cdot \\mathbf{u}_S = \\nabla \\cdot (\\nabla \\times \\mathbf{A}) = 0<\/code><\/div>\n

                          \uff08\u767a\u6563\u30bc\u30ed\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                        • \n
                          \n
                          \u2207\u00d7uS=\u2207\u00d7(\u2207\u00d7A)\u22600\\nabla \\times \\mathbf{u}_S = \\nabla \\times (\\nabla \\times \\mathbf{A}) \\neq 0<\/span>\\nabla \\times \\mathbf{u}_S = \\nabla \\times (\\nabla \\times \\mathbf{A}) \\neq 0<\/code><\/div>\n

                          \uff08\u56de\u8ee2\u975e\u30bc\u30ed\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                        • \n
                          \n
                          A\\mathbf{A}<\/span>\\mathbf{A}<\/code><\/div>\n

                          \u306f\u6ce2\u52d5\u65b9\u7a0b\u5f0f <\/span><\/span><\/p>\n

                          \u2202t2A=vS2\u0394A\\partial_t^2 \\mathbf{A} = v_S^2 \\Delta \\mathbf{A}<\/span>\\partial_t^2 \\mathbf{A} = v_S^2 \\Delta \\mathbf{A}<\/code><\/div>\n

                          \u3092\u6e80\u305f\u3059\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

                          (3) \u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u8a08\u7b97<\/span><\/span><\/div>\n
                            \n
                          • \n
                            \n
                            \u03d5\\phi<\/span>\\phi<\/code><\/div>\n

                            \u306f\u3001\u767a\u6563 <\/span><\/span><\/p>\n

                            \u2207\u22c5u\\nabla \\cdot \\mathbf{u}<\/span>\\nabla \\cdot \\mathbf{u}<\/code><\/div>\n

                            \u304b\u3089\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f <\/span><\/span><\/p>\n

                            \u0394\u03d5=\u2207\u22c5u\\Delta \\phi = \\nabla \\cdot \\mathbf{u}<\/span>\\Delta \\phi = \\nabla \\cdot \\mathbf{u}<\/code><\/div>\n

                            \u3092\u89e3\u3044\u3066\u5f97\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n

                          • \n
                            \n
                            A\\mathbf{A}<\/span>\\mathbf{A}<\/code><\/div>\n

                            \u306f\u3001\u56de\u8ee2 <\/span><\/span><\/p>\n

                            \u2207\u00d7u\\nabla \\times \\mathbf{u}<\/span>\\nabla \\times \\mathbf{u}<\/code><\/div>\n

                            \u304b\u3089 <\/span><\/span><\/p>\n

                            \u0394A=\u2212\u2207\u00d7u\\Delta \\mathbf{A} = -\\nabla \\times \\mathbf{u}<\/span>\\Delta \\mathbf{A} = -\\nabla \\times \\mathbf{u}<\/code><\/div>\n

                            \u3092\u89e3\u304f\uff08Coulomb gauge <\/span><\/span><\/p>\n

                            \u2207\u22c5A=0\\nabla \\cdot \\mathbf{A} = 0<\/span>\\nabla \\cdot \\mathbf{A} = 0<\/code><\/div>\n

                            \u3092\u8ab2\u3059\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                          • \n
                            \u5b9f\u969b\u306b\u306f\u3001\u5730\u9707\u6ce2\u306e\u6642\u9593\u4f9d\u5b58\u6027\uff08\u6ce2\u52d5\u4f1d\u64ad\uff09\u3092\u8003\u616e\u3057\u3001\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u65b9\u7a0b\u5f0f\u3084\u30d5\u30fc\u30ea\u30a8\u89e3\u6790\u3092\u7528\u3044\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n
                            \n
                            4. \u5177\u4f53\u4f8b\uff1a\u5730\u9707\u6ce2\u306e\u5206\u96e2<\/span><\/span><\/div>\n
                            \u30b7\u30ca\u30ea\u30aa<\/span><\/span>\uff1a\u5730\u9707\u89b3\u6e2c\u70b9\u3067\u8a18\u9332\u3055\u308c\u305f\u5909\u4f4d\u5834 <\/span><\/span><\/p>\n
                            u(x,t)\\mathbf{u}(\\mathbf{x}, t)<\/span>\\mathbf{u}(\\mathbf{x}, t)<\/code><\/div>\n

                            \u3092P\u6ce2\u3068S\u6ce2\u306b\u5206\u96e2\u3059\u308b\u3002<\/span><\/span><\/div>\n

                              \n
                            1. \n
                              \u30c7\u30fc\u30bf\u306e\u53d6\u5f97<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                \n
                              • \n
                                \u5730\u9707\u8a08\u30673\u6210\u5206\uff08x, y, z\uff09\u306e\u5909\u4f4d <\/span><\/span><\/p>\n
                                u=(ux,uy,uz)\\mathbf{u} = (u_x, u_y, u_z)<\/span>\\mathbf{u} = (u_x, u_y, u_z)<\/code><\/div>\n

                                \u3092\u6e2c\u5b9a\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n

                              • \n
                                \u767a\u6563\u3068\u56de\u8ee2\u306e\u8a08\u7b97<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                  \n
                                • \n
                                  \u767a\u6563\uff1a<\/span><\/span><\/p>\n
                                  \u2207\u22c5u=\u2202xux+\u2202yuy+\u2202zuz\\nabla \\cdot \\mathbf{u} = \\partial_x u_x + \\partial_y u_y + \\partial_z u_z<\/span>\\nabla \\cdot \\mathbf{u} = \\partial_x u_x + \\partial_y u_y + \\partial_z u_z<\/code><\/div>\n

                                  \uff08P\u6ce2\u306e\u5f37\u5ea6\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                                • \n
                                  \u56de\u8ee2\uff1a<\/span><\/span><\/p>\n
                                  \u2207\u00d7u=(\u2202yuz\u2212\u2202zuy,\u2202zux\u2212\u2202xuz,\u2202xuy\u2212\u2202yux)\\nabla \\times \\mathbf{u} = (\\partial_y u_z – \\partial_z u_y, \\partial_z u_x – \\partial_x u_z, \\partial_x u_y – \\partial_y u_x)<\/span>\\nabla \\times \\mathbf{u} = (\\partial_y u_z - \\partial_z u_y, \\partial_z u_x - \\partial_x u_z, \\partial_x u_y - \\partial_y u_x)<\/code><\/div>\n

                                  \uff08S\u6ce2\u306e\u5f37\u5ea6\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n

                                • \n
                                  \u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u89e3<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                    \n
                                  • \n
                                    \n
                                    \u03d5\\phi<\/span>\\phi<\/code><\/div>\n

                                    \u3092 <\/span><\/span><\/p>\n

                                    \u0394\u03d5=\u2207\u22c5u\\Delta \\phi = \\nabla \\cdot \\mathbf{u}<\/span>\\Delta \\phi = \\nabla \\cdot \\mathbf{u}<\/code><\/div>\n

                                    \u304b\u3089\u8a08\u7b97\uff08\u4f8b\uff1a\u30b0\u30ea\u30fc\u30f3\u95a2\u6570\u3084\u6570\u5024\u89e3\u6cd5\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n

                                  • \n
                                    \n
                                    A\\mathbf{A}<\/span>\\mathbf{A}<\/code><\/div>\n

                                    \u3092 <\/span><\/span><\/p>\n

                                    \u0394A=\u2212\u2207\u00d7u\\Delta \\mathbf{A} = -\\nabla \\times \\mathbf{u}<\/span>\\Delta \\mathbf{A} = -\\nabla \\times \\mathbf{u}<\/code><\/div>\n

                                    \u304b\u3089\u8a08\u7b97\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n

                                  • \n
                                    \u6ce2\u306e\u5206\u96e2<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                      \n
                                    • \n
                                      P\u6ce2\uff1a<\/span><\/span><\/p>\n
                                      uP=\u2207\u03d5\\mathbf{u}_P = \\nabla \\phi<\/span>\\mathbf{u}_P = \\nabla \\phi<\/code><\/div>\n

                                      \u3001\u4f1d\u64ad\u901f\u5ea6 <\/span><\/span><\/p>\n

                                      vPv_P<\/span>v_P<\/code><\/div>\n

                                      \u3001\u7e26\u6ce2\u3002<\/span><\/span><\/div>\n<\/li>\n

                                    • \n
                                      S\u6ce2\uff1a<\/span><\/span><\/p>\n
                                      uS=\u2207\u00d7A\\mathbf{u}_S = \\nabla \\times \\mathbf{A}<\/span>\\mathbf{u}_S = \\nabla \\times \\mathbf{A}<\/code><\/div>\n

                                      \u3001\u4f1d\u64ad\u901f\u5ea6 <\/span><\/span><\/p>\n

                                      vSv_S<\/span>v_S<\/code><\/div>\n

                                      \u3001\u6a2a\u6ce2\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                                      \u4f8b\uff1a\u70b9\u9707\u6e90<\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                        \n
                                      • \n
                                        \u70b9\u9707\u6e90\uff08\u4f8b\uff1a\u65ad\u5c64\u306e\u7834\u58ca\uff09\u3067\u306f\u3001<\/span><\/span><\/p>\n
                                        u\\mathbf{u}<\/span>\\mathbf{u}<\/code><\/div>\n

                                        \u306f\u653e\u5c04\u72b6\uff08P\u6ce2\uff09\u3068\u63a5\u7dda\u65b9\u5411\uff08S\u6ce2\uff09\u306e\u6210\u5206\u3092\u6301\u3064\u3002<\/span><\/span><\/div>\n<\/li>\n

                                      • \n
                                        \u30db\u30c3\u30b8\u5206\u89e3\u306b\u3088\u308a\u3001\u9060\u65b9\u5834\u3067P\u6ce2\u304c\u653e\u5c04\u65b9\u5411\u3001S\u6ce2\u304c\u76f4\u4ea4\u65b9\u5411\u306b\u5206\u96e2\u3055\u308c\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n
                                        \n
                                        5. \u5fdc\u7528\u4f8b<\/span><\/span><\/div>\n
                                        \u30db\u30c3\u30b8\u5206\u89e3\u306f\u3001\u5730\u9707\u5b66\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5fdc\u7528\u3055\u308c\u307e\u3059\uff1a<\/span><\/span><\/div>\n
                                          \n
                                        1. \n
                                          \u5730\u9707\u6ce2\u306e\u5206\u96e2\u3068\u89e3\u6790<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                            \n
                                          • \n
                                            \u89b3\u6e2c\u30c7\u30fc\u30bf\u304b\u3089P\u6ce2\u3068S\u6ce2\u3092\u5206\u96e2\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u5230\u9054\u6642\u9593\u3084\u632f\u5e45\u3092\u89e3\u6790\u3002<\/span><\/span><\/div>\n<\/li>\n
                                          • \n
                                            \u4f8b\uff1aP\u6ce2\u306e\u5230\u9054\u6642\u9593\u3067\u9707\u6e90\u4f4d\u7f6e\u3092\u7279\u5b9a\u3001S\u6ce2\u3067\u305b\u3093\u65ad\u5fdc\u529b\u3092\u8a55\u4fa1\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n
                                          • \n
                                            \u5730\u7403\u5185\u90e8\u69cb\u9020\u306e\u63a8\u5b9a<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                              \n
                                            • \n
                                              P\u6ce2\u3068S\u6ce2\u306e\u901f\u5ea6\u5dee\uff08<\/span><\/span><\/p>\n
                                              vP\/vSv_P\/v_S<\/span>v_P\/v_S<\/code><\/div>\n

                                              \uff09\u304b\u3089\u3001\u5730\u7403\u5185\u90e8\u306e\u5f3e\u6027\u4fc2\u6570\uff08<\/span><\/span><\/p>\n

                                              \u03bb,\u03bc\\lambda, \\mu<\/span>\\lambda, \\mu<\/code><\/div>\n

                                              \uff09\u3084\u5bc6\u5ea6\u3092\u63a8\u5b9a\u3002<\/span><\/span><\/div>\n<\/li>\n

                                            • \n
                                              \u30db\u30c3\u30b8\u5206\u89e3\u3067\u5206\u96e2\u3057\u305f\u6210\u5206\u3092\u7528\u3044\u3066\u3001\u30c8\u30e2\u30b0\u30e9\u30d5\u30a3\u30fc\uff08\u5730\u9707\u6ce2\u30c8\u30e2\u30b0\u30e9\u30d5\u30a3\u30fc\uff09\u3067\u5730\u4e0b\u69cb\u9020\u3092\u53ef\u8996\u5316\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n
                                            • \n
                                              \u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                                \n
                                              • \n
                                                \u5730\u9707\u6ce2\u306e\u4f1d\u64ad\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3059\u308b\u969b\u3001\u30db\u30c3\u30b8\u5206\u89e3\u3092\u7528\u3044\u3066P\u6ce2\u3068S\u6ce2\u3092\u500b\u5225\u306b\u30e2\u30c7\u30eb\u5316\u3002<\/span><\/span><\/div>\n<\/li>\n
                                              • \n
                                                \u4f8b\uff1a\u6709\u9650\u8981\u7d20\u6cd5\u3084\u30b9\u30da\u30af\u30c8\u30eb\u6cd5\u3067\u3001<\/span><\/span><\/p>\n
                                                \u03d5,A\\phi, \\mathbf{A}<\/span>\\phi, \\mathbf{A}<\/code><\/div>\n

                                                \u306e\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n

                                              • \n
                                                \u8868\u9762\u6ce2\u306e\u89e3\u6790<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                                  \n
                                                • \n
                                                  \u8868\u9762\u6ce2\uff08Rayleigh\u6ce2\u306a\u3069\uff09\u306fP\u6ce2\u3068S\u6ce2\u306e\u6df7\u5408\u3002\u30db\u30c3\u30b8\u5206\u89e3\u3092\u62e1\u5f35\u3057\u3001\u6df1\u3055\u65b9\u5411\u306e\u5909\u4f4d\u3092\u5206\u96e2\u3002<\/span><\/span><\/div>\n<\/li>\n
                                                • \n
                                                  \u4f8b\uff1aRayleigh\u6ce2\u306e\u5206\u6563\u66f2\u7dda\u304b\u3089\u5730\u6bbb\u69cb\u9020\u3092\u63a8\u5b9a\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n
                                                • \n
                                                  \u30ce\u30a4\u30ba\u9664\u53bb<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n
                                                    \n
                                                  • \n
                                                    \u5730\u9707\u89b3\u6e2c\u30c7\u30fc\u30bf\u306b\u306f\u30ce\u30a4\u30ba\uff08\u4f8b\uff1a\u98a8\u3084\u6d77\u6d0b\u6ce2\uff09\u304c\u542b\u307e\u308c\u308b\u3002\u30db\u30c3\u30b8\u5206\u89e3\u3067\u767a\u6563\u30bc\u30ed\u6210\u5206\uff08S\u6ce2\uff09\u3084\u56de\u8ee2\u30bc\u30ed\u6210\u5206\uff08P\u6ce2\uff09\u3092\u5f37\u8abf\u3057\u3001\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n
                                                    \n
                                                    6. \u9ad8\u6b21\u5143\u3068\u306e\u95a2\u9023<\/span><\/span><\/div>\n
                                                    \u5730\u9707\u5b66\u3067\u306f\u901a\u5e383\u6b21\u5143\uff08<\/span><\/span><\/p>\n
                                                    R3\\mathbb{R}^3<\/span>\\mathbb{R}^3<\/code><\/div>\n

                                                    \uff09\u3092\u6271\u3044\u307e\u3059\u304c\u3001\u9ad8\u6b21\u5143\u3078\u306e\u62e1\u5f35\u3082\u7406\u8ad6\u7684\u306b\u53ef\u80fd\u3067\u3059\uff1a<\/span><\/span><\/div>\n

                                                      \n
                                                    • \n
                                                      4D\u89e3\u6790\uff08\u6642\u7a7a\uff09<\/span><\/span><\/span>\uff1a\u6642\u9593\u4f9d\u5b58\u6027\u30924\u6b21\u5143\u76ee\u3068\u307f\u306a\u3057\u30014D\u30d9\u30af\u30c8\u30eb\u5834 <\/span><\/span><\/p>\n
                                                      u(x,t)\\mathbf{u}(\\mathbf{x}, t)<\/span>\\mathbf{u}(\\mathbf{x}, t)<\/code><\/div>\n

                                                      \u3092\u5206\u89e3\u3002\u6642\u9593\u767a\u5c55\u3092\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3084\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u3067\u51e6\u7406\u3002<\/span><\/span><\/div>\n<\/li>\n

                                                    • \n
                                                      \u30c6\u30f3\u30bd\u30eb\u5834<\/span><\/span><\/span>\uff1a\u5fdc\u529b\u30c6\u30f3\u30bd\u30eb\u3084\u6b6a\u30c6\u30f3\u30bd\u30eb\u3092\u9ad8\u6b21\u5143\u30db\u30c3\u30b8\u5206\u89e3\u3067\u89e3\u6790\uff08\u4f8b\uff1a4\u6b21\u5143\u6642\u7a7a\u3067\u306e\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u5730\u9707\u30e2\u30c7\u30eb\uff09\u3002<\/span><\/span><\/div>\n<\/li>\n
                                                    • \n
                                                      \u30ab\u30e9\u30d3-\u30e4\u30a6\u3068\u306e\u95a2\u9023<\/span><\/span><\/span>\uff1a\u76f4\u63a5\u7684\u3067\u306f\u306a\u3044\u304c\u3001\u5f26\u7406\u8ad6\u3067\u30ab\u30e9\u30d3-\u30e4\u30a6\u591a\u69d8\u4f53\u4e0a\u306e\u6ce2\u52d5\u89e3\u6790\u304c\u5730\u9707\u6ce2\u306e\u6570\u5b66\u7684\u30a2\u30ca\u30ed\u30b8\u30fc\u3068\u3057\u3066\u7814\u7a76\u3055\u308c\u308b\u5834\u5408\u3001\u30db\u30c3\u30b8\u5206\u89e3\u304c\u5fdc\u7528\u3055\u308c\u308b\u3002<\/span><\/span><\/div>\n<\/li>\n<\/ul>\n
                                                      \n
                                                      7. \u6570\u5b66\u7684\u8a73\u7d30<\/span><\/span><\/div>\n
                                                      \u30db\u30c3\u30b8\u5206\u89e3\u3092\u5730\u9707\u6ce2\u306b\u9069\u7528\u3059\u308b\u969b\u306e\u8a08\u7b97\u624b\u9806\uff1a<\/span><\/span><\/div>\n
                                                        \n
                                                      1. \n
                                                        \u767a\u6563\u3068\u56de\u8ee2\u306e\u62bd\u51fa<\/span><\/span><\/span>\uff1a<\/span><\/span><\/div>\n