\u3000\u4ee5\u4e0b\u306e \u5909\u63db\u5f0f<\/em> \u306f<\/p>\n

$x = f(u_1, u_2, u_3)\\ y = g(u_1, u_2, u_3)\\ z = h(u_1, u_2, u_3)\\cdots(17)$ <\/p>\n

\u3053\u3053\u3067\u4ee5\u4e0b\u306e\u524d\u63d0\u3092\u7f6e\u304d\u307e\u3059\uff0e\u3064\u307e\u308a $f$ , $g$ , $h$ \u306f\u9023\u7d9a\u3067\u3042\u308a\uff0c\u9023\u7d9a\u306a\u504f\u5fae\u5206\u3092\u6709\u3057\uff0c\u76f4\u4ea4\u5ea7\u6a19\u7cfb $xyz$ \u3068 $u_1u_2u_3$ \u3068\u306e\u9593\u3067\u70b9\u304c 1 \u5bfe 1 \u306b\u5bfe\u5fdc\u3059\u308b\u5358\u4e00\u306e\u9006\u95a2\u6570\u304c\u78ba\u7acb\u3057\u3066\u3044\u308b\u3068\u3057\u307e\u3059\uff0e\u30d9\u30af\u30c8\u30eb\u8a18\u6cd5\u306b\u304a\u3044\u3066\u306f\u5909\u63db\u5f0f (17) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u307e\u3059\uff0e<\/p>\n

$\\bold{r} = x\\bold{i} + y\\bold{j} + z\\bold{k} = f(u_1, u_2, u_3)\\bold{i} + g(u_1, u_2, u_3)\\bold{j} + h(u_1, u_2, u_3)\\bold{k}\\cdots (18)$ <\/p>\n

\u3000\u3042\u308b\u70b9 $P$ \u306f \u76f4\u4ea4\u5ea7\u6a19<\/em> $(x, y, z)$ \u3060\u3051\u3067\u5b9a\u7fa9\u51fa\u6765\u308b\u3060\u3051\u3067\u306a\u304f\uff0c\u5ea7\u6a19 $(u_1, u_2, u_3)$ \u306b\u3088\u3063\u3066\u3082\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e\u3053\u306e $(u_1, u_2, u_3)$ \u3092\u305d\u306e\u70b9\u306e \u66f2\u7dda\u5ea7\u6a19<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n

\u3000\u4eee\u306b $u_2$ \u304a\u3088\u3073 $u_3$ \u304c\u5b9a\u6570\u3067\u3042\u308a\uff0c $u_1$ \u304c\u5909\u5316\u3059\u308b\u3068\uff0c $\\bold{r}$ \u306f u_{1<\/sub> \u5ea7\u6a19\u66f2\u7dda<\/em> \u3068\u547c\u3070\u308c\u308b\u66f2\u7dda\u3092\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u540c\u69d8\u306b \u3092\u901a\u308b \u304a\u3088\u3073 \u5ea7\u6a19\u66f2\u7dda\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n}

\u3000\u5f0f (18) \u304b\u3089\u4ee5\u4e0b\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n

$\\displaystyle d\\bold{r} = \\frac{\\partial\\bold{r}}{\\partial u_1}du_1 + \\frac{\\partial\\bold{r}}{\\partial u_2}du_2 + \\frac{\\partial\\bold{r}}{\\partial u_3}du_3 \\cdots (19)$ <\/p>\n

\u3000\u30d9\u30af\u30c8\u30eb $\\partial\\bold{r}\/\\partial u_1$ \u306f\u70b9 $P$ \u306b\u304a\u3051\u308b $u_1$ \u5ea7\u6a19\u66f2\u7dda\u3078\u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u3067\u3059\uff0e\u4eee\u306b $\\bold{e_1}$ \u304c\u70b9 $P$ \u306b\u304a\u3051\u308b\u3053\u306e\u65b9\u5411\u3078\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306a\u3089\u3053\u306e\u3088\u3046\u306b\u66f8\u3051\u307e\u3059\uff0c $\\partial \\bold{r} \/ \\partial u_1 = h_1\\bold{e_1}$ \u3068\uff0e\u3053\u3053\u3067 $h_1 = |\\partial\\bold{r}\/\\partial u_1|$ \u3067\u3059\uff0e\u540c\u69d8\u306b\u6b21\u306e\u3088\u3046\u306b\u66f8\u3051\u307e\u3059\uff0e $\\partial\\bold{r} \/ \\partial u_2 = h_2\\bold{e_2}$ \u307e\u305f $\\partial\\bold{r}\/\\partial u_3 = h_3 \\bold{e_3}$ \u3053\u3053\u3067\uff0c\u305d\u308c\u305e\u308c $h_2 = |\\partial\\bold{r}\/\\partial u_2|$ \u307e\u305f $h_3 = |\\partial\\bold{r}\/\\partial u_3|$ \u3067\u3059\uff0e\u3086\u3048\u306b\u5f0f (19) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u307e\u3059\uff0e<\/p>\n

$d\\bold{r} = h_1du\\bold{e_1} + h_2du\\bold{e_2} + h_3du\\bold{e_3}\\cdots(20)$ <\/p>\n

\u3000\u91cf $h_1$ , $h_2$ , $h_3$ \u306f\u6642\u306b \u30b9\u30b1\u30fc\u30eb\u56e0\u5b50<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n

\u3000\u4eee\u306b $\\bold{e_1}$ , $\\bold{e_2}$ , $\\bold{e_3}$ \u304c\u70b9 $P$ \u306b\u304a\u3044\u3066\u76f8\u4e92\u306b\u5782\u76f4\u3068\u3059\u308b\u3068\uff0c\u305d\u306e\u66f2\u7dda\u5ea7\u6a19\u3092 \u76f4\u4ea4<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u5f27\u9577\u306e\u8981\u7d20 $ds$ \u306f\u4ee5\u4e0b\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u307e\u3059\uff0e<\/p>\n

$ds^2 = d\\bold{r} \\cdot d\\bold{r} = h_1^2du_1^2 + h_2^2du_2^2 + h_3^2du_3^2 \\cdots(21)$ <\/p>\n

\u307e\u305f\u4e0a\u8a18\u306e\u76f4\u65b9\u4f53\u306e\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u306e2\u4e57\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff0e<\/p>\n

\u3000\u307e\u305f\uff0c\u76f4\u4ea4\u5ea7\u6a19\u306b\u304a\u3044\u3066\u306f\u76f4\u65b9\u4f53\u306e\u4f53\u7a4d\u306f\u4ee5\u4e0b\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u307e\u3059\uff0e<\/p>\n

$dV = |(h_1du_1\\bold{e_1}) \\cdot (h_2du_2\\bold{e_2}) \\times (h_3du_3\\bold{e_3})| = h_1h_2h_3du_1du_2du_3 \\cdots (22)$ <\/p>\n

\u3053\u3053\u3067\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3067\u304d\u307e\u3059\uff0e<\/p>\n

$\\displaystyle dV = \\left| \\frac{\\partial\\bold{r}}{\\partial u_1} \\cdot \\frac{\\partial\\bold{r}}{\\partial u_2} \\times \\frac{\\partial\\bold{r}}{\\partial u_3} \\right| du_1du_2du_3 = \\left| \\frac{\\partial(x, y, z)}{\\partial(u_1, u_2, u_3)} \\right|du_1du_2du_3 \\cdots (23)$ <\/p>\n

\u3053\u3053\u3067\uff0c<\/p>\n

$\\displaystyle \\frac{\\partial(x, y, z)}{\\partial(u_1, u_2, u_3)} = \\left| \\begin{array}{ccc} \\frac{\\partial x}{\\partial u_1} & \\frac{\\partial x}{\\partial u_2} & \\frac{\\partial x}{\\partial u_3} \\\\ \\frac{\\partial y}{\\partial u_1} & \\frac{\\partial y}{\\partial u_2} & \\frac{\\partial y}{\\partial u_3} \\\\ \\frac{\\partial z}{\\partial u_1} & \\frac{\\partial z}{\\partial u_2} & \\frac{\\partial z}{\\partial u_3} \\end{array} \\right|\\cdots (24)$ <\/p>\n

\u4e0a\u8a18\u306f\u5909\u63db\u5f0f\u306e \u30e4\u30b3\u30d3\u30a2\u30f3<\/em> \u3068\u547c\u3070\u308c\u307e\u3059\uff0e<\/p>\n

\u3000\u30e4\u30b3\u30d3\u30a2\u30f3\u304c\u30bc\u30ed\u306b\u7b49\u3057\u3044\u6642\u306b\u76f4\u65b9\u4f53\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u306b\u306f $x$ , $y$ \u304a\u3088\u3073 $z$ \u306e\u9593\u306b\u306f\u95a2\u6570\u95a2\u4fc2\u304c\u5b58\u5728\u3057\u307e\u3059\uff0e\u4f8b\u3048\u3070 $\\phi$ \u304c\u3042\u3063\u3066\uff0c $\\phi(x, y, z) = 0$ \u306e\u3088\u3046\u306a\u5834\u5408\u3067\u3059\uff0e<\/p>\n

<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u4ee5\u4e0b\u306e \u5909\u63db\u5f0f \u306f \u3053\u3053\u3067\u4ee5\u4e0b\u306e\u524d\u63d0\u3092\u7f6e\u304d\u307e\u3059\uff0e\u3064\u307e\u308a , , \u306f\u9023\u7d9a\u3067\u3042\u308a\uff0c\u9023\u7d9a\u306a\u504f\u5fae\u5206\u3092\u6709\u3057\uff0c\u76f4\u4ea4\u5ea7\u6a19\u7cfb \u3068 \u3068\u306e\u9593\u3067\u70b9\u304c 1 \u5bfe 1 \u306b\u5bfe\u5fdc\u3059\u308b\u5358\u4e00\u306e\u9006\u95a2\u6570\u304c\u78ba\u7acb\u3057\u3066\u3044\u308b\u3068\u3057\u307e\u3059\uff0e\u30d9\u30af\u30c8\u30eb\u8a18\u6cd5\u306b\u304a\u3044\u3066\u306f\u5909\u63db\u5f0f ( … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5343\" class=\"more-link\"><span class=\"screen-reader-text\">“\u76f4\u4ea4\u66f2\u7dda\u5ea7\u6a19\u3068\u30e4\u30b3\u30d3\u30a2\u30f3” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-5343","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5343"}],"version-history":[{"count":10,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5343\/revisions"}],"predecessor-version":[{"id":6776,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5343\/revisions\/6776"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}