{"id":5778,"date":"2014-09-29T06:00:05","date_gmt":"2014-09-28T21:00:05","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5778"},"modified":"2014-09-29T17:32:59","modified_gmt":"2014-09-29T08:32:59","slug":"post-5778","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5778","title":{"rendered":"\u9762\u7a4d\u5206"},"content":{"rendered":"
\"Fig.<\/a>
Fig. 6-3<\/figcaption><\/figure>\n

\u3000S \u3092 Fig. 6-3 \u306b\u793a\u3059\u3088\u3046\u306b xy \u5e73\u9762\u3078\u306e\u5c04\u5f71 \\cal R \u3092\u6709\u3059\u308b\u8868\u88cf\u306e\u3042\u308b\u9762\u3068\u3057\u307e\u3059\uff0e S \u3092\u8868\u3059\u5f0f\u3092 z = f(x, y) \u3068\u3057\uff0c f \u306f\u5358\u4e00\u5024\u3067\uff0c\\cal R \u306b\u304a\u3044\u3066\u5168\u3066\u306e x \u304a\u3088\u3073 y \u306b\u3064\u3044\u3066\u9023\u7d9a\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\uff0e \\cal R \u3092 n \u500b\u306e\u9818\u57df \\Delta A_p,\\ p = 1,\\ 2,\\ \\dots,\\ n \u306b\u7d30\u5206\u5316\u3057\uff0c\u5404\u3005\u306e\u5c0f\u9818\u57df\u306e\u4e0a\u306b\u5782\u76f4\u306a\u67f1\u3092\u7acb\u3066\uff0c\u9818\u57df \\Delta S_p \u306b\u304a\u3044\u3066 S \u3068\u4ea4\u5dee\u3055\u305b\u307e\u3059\uff0e<\/p>\n

\u3000 \\phi (x, y, z) \u3092\u5358\u4e00\u5024\u3067 S \u4e0a\u306e\u3042\u3089\u3086\u308b\u70b9\u3067\u9023\u7d9a\u3067\u3042\u308b\u3068\u3057\u307e\u3059\uff0e\u6b21\u306e\u548c\u3092\u8003\u3048\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\sum_{p=1}^{n}\\phi(\\xi_p, \\eta_p, \\zeta_p)\\Delta S_p \\cdots(29)<\/p>\n

\u3053\u3053\u3067 (\\xi_p, \\eta_p, \\zeta_p) \u306f \\Delta S_p \u4e0a\u306e\u4efb\u610f\u306e\u70b9\u3067\u3059\uff0e\u4eee\u306b n \\rightarrow \\infty \u306e\u6642\u5404\u3005\u306e \\Delta S_p \\rightarrow 0 \u3068\u306a\u308b\u3053\u306e\u548c\u306e\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089\uff0c\u7d50\u679c\u306e\u6975\u9650\u306f \\phi(x, y, z) \u306e S \u4e0a\u306e \u9762\u7a4d\u5206<\/em> \u3068\u547c\u3070\u308c\uff0c\u4ee5\u4e0b\u306b\u3088\u308a\u6307\u5b9a\u3055\u308c\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)dS\\cdots(30)<\/p>\n

\u3000\u304a\u3088\u305d \\Delta S_p = |\\sec\\gamma_p|\\Delta A_p \u3067\u3042\u308b\u305f\u3081\uff0c\u3053\u3053\u3067 \\gamma_p \u306f S \u3078\u306e\u6cd5\u7dda\u304a\u3088\u3073 z \u8ef8\u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308a\uff0c\u548c (29) \u306e\u6975\u9650\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)|\\sec\\gamma|dA\\cdots(31)<\/p>\n

\u3000 |\\sec\\gamma| \u306e\u5927\u304d\u3055\u306f\u4ee5\u4e0b\u3067\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n

\\displaystyle |\\sec\\gamma| = \\frac{1}{|\\bold{n}_p\\cdot\\bold{k}|} = \\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}\\cdots(32)<\/p>\n

\u3000\u305d\u3053\u3067 x = f(x, y) \u306f \\cal R \u306b\u304a\u3044\u3066\u9023\u7d9a\uff08\u53c8\u306f\u533a\u9593\u7684\u306b\u9023\u7d9a\uff09\u306a\u5fae\u5206\u4fc2\u6570\u3092\u6709\u3057\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068 (31) \u306f\u76f4\u4ea4\u7cfb\u306b\u304a\u3044\u3066\u306f\u6b21\u306e\u5f62\u3067\u8a18\u8ff0\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)\\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}dxdy \\cdots(33)<\/p>\n

\u3000 S \u306e\u5f0f\u304c F(x, y, z) = 0 \u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u5834\u5408\u306f (33) \u306f\u6b21\u306e\u5f62\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)\\frac{\\sqrt{(F_x)^2 + (F_y)^2 + (F_z)^2}}{|F_z|}dxdy\\cdots(34)<\/p>\n

\u3000\u305d\u306e\u7d50\u679c (33) \u307e\u305f\u306f (34) \u306f (30) \u3092\u8a55\u4fa1\u3059\u308b\u306e\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\u3000\u4e0a\u8a18\u306b\u304a\u3044\u3066\u306f S \u306f z \u8ef8\u306b\u5e73\u884c\u306a\u3044\u304b\u306a\u308b\u7dda\u3082\u9762 S \u3068\u305f\u3060 1 \u70b9\u306b\u304a\u3044\u3066\u4ea4\u5dee\u3059\u308b\u3088\u3046\u306a\u9762\u3067\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u307e\u3059\uff0e\u9762 S \u304c\u3053\u306e\u30bf\u30a4\u30d7\u3067\u306a\u3044\u4f8b\u306b\u304a\u3044\u3066\u306f\uff0c\u666e\u901a S \u3092 S_1,\\ S_2,\\ \\dots \u306b\u5206\u5272\u3057\u3066\u3053\u306e\u30bf\u30a4\u30d7\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u305d\u3053\u3067\u9762 S \u4e0a\u306e\u9762\u7a4d\u5206\u3092 S_1,\\ S_2,\\ \\dots \u4e0a\u306e\u9762\u7a4d\u5206\u306e\u548c\u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\u3000\u3053\u306e\u7d50\u679c\u306f S \u304c xy \u5e73\u9762 \u306b\u304a\u3051\u308b\u9818\u57df \\cal R \u3078\u306e\u5c04\u5f71\u306e\u6642\u4fdd\u6301\u3055\u308c\u307e\u3059\uff0e\u5834\u5408\u306b\u3088\u3063\u3066\u306f S \u3092 yz \u307e\u305f\u306f xz \u5e73\u9762\u306b\u5c04\u5f71\u3057\u305f\u307b\u3046\u304c\u826f\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u306f (30) \u306f (33) \u304a\u3088\u3073 (34) \u3092\u9069\u5207\u306b\u4fee\u6b63\u3059\u308b\u3053\u3068\u3067\u8a55\u4fa1\u3055\u308c\u307e\u3059\uff0e<\/p>\n