{"id":6535,"date":"2023-06-16T10:24:03","date_gmt":"2023-06-16T01:24:03","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=6535"},"modified":"2023-06-16T10:44:53","modified_gmt":"2023-06-16T01:44:53","slug":"%e6%a5%95%e5%86%86%e3%81%ae%e5%91%a8%e9%95%b7%e3%82%92%e4%b8%80%e5%ae%9a%e3%81%ab%e3%81%97%e3%81%9f%e3%81%a8%e3%81%8d%ef%bc%8c%e9%9d%a2%e7%a9%8d%e3%81%8c%e6%9c%80%e5%a4%a7%e3%81%a8%e3%81%aa%e3%82%8b","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6535\/","title":{"rendered":"\u6955\u5186\u306e\u5468\u9577\u3092\u4e00\u5b9a\u306b\u3057\u305f\u3068\u304d\uff0c\u9762\u7a4d\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\u5186\u3067\u3042\u308b\u3053\u3068\u306e\u8fd1\u4f3c\u7684\u8a3c\u660e"},"content":{"rendered":"<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%81%8f%e5%be%ae%e5%88%86%ef%bc%9a%e5%a4%9a%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e9%99%b0%e9%96%a2%e6%95%b0%e5%ae%9a%e7%90%86\/\">\u9670\u95a2\u6570\u5b9a\u7406<\/a>\u306e\u7df4\u7fd2\u554f\u984c\u3068\u3057\u3066\u3002<!--more--><\/p>\n<h3>\u7df4\u7fd2\u554f\u984c\uff1a\u9577\u65b9\u5f62\u306e\u5468\u9577\u3092\u4e00\u5b9a\u306b\u3057\u305f\u3068\u304d\uff0c\u9762\u7a4d\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\u6b63\u65b9\u5f62\u306e\u3068\u304d\u3067\u3042\u308b\u3053\u3068<\/h3>\n<p>\u7e26\u6a2a\u306e\u9577\u3055\u304c\u305d\u308c\u305e\u308c $a, b$ \u3067\u3042\u308b\u9577\u65b9\u5f62\u306e\u5468\u306e\u9577\u3055 $L$ \u306f<\/p>\n<p>$$L = 2(a+b)$$<\/p>\n<p>\u3067\u3042\u308a\uff0c\u9762\u7a4d $S$ \u306f<\/p>\n<p>$$S = a b$$<\/p>\n<p>\u5468\u9577 $L$ \u3092\u4e00\u5b9a\u306b\u4fdd\u3063\u305f\u307e\u307e $a, b$ \u3092\u5909\u5316\u3055\u305b\u308b\u3068\uff0c\u9762\u7a4d $S$ \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $a = b = \\frac{L}{4}$ \u306e\u6b63\u65b9\u5f62\u306e\u3068\u304d\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6563\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/choho1.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<p>\u5f8c\u3005\u306e\u5fdc\u7528\u3092\u8003\u3048\u3066\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u9670\u95a2\u6570\u5b9a\u7406<\/strong><\/span>\u306a\u3093\u304b\u3092\u4f7f\u3063\u3066\u5927\u639b\u304b\u308a\u7684\u306b\u3084\u308b\u3002\u307e\u305a\uff0c$L = \\mbox{const.} \\equiv L_0$\u00a0 \u3067\u3042\u308b\u306e\u3067\uff0c$a, b$ \u306f\u3069\u3061\u3089\u3082\u72ec\u7acb\u306a\u5909\u6570\u3068\u3044\u3046\u308f\u3051\u306b\u306f\u3044\u304b\u306a\u304f\u306a\u308a\uff0c$b$ \u306f $a$ \u306e\u95a2\u6570 $b = b(a)$ \u3068\u306a\u308b\u3002\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u3066\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{db}{da} &amp;=&amp; &#8211; \\frac{\\frac{\\partial L}{\\partial a}}{\\frac{\\partial L}{\\partial b}} \\\\<br \/>\n&amp;=&amp; &#8211; \\frac{2}{2} = -1<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u6761\u4ef6\u306e\u3082\u3068\u3067\uff0c$S$ \u304c\u6975\u5024\uff08\u6700\u5927\u5024\uff09\u3092\u6301\u3064\u306e\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{dS}{da} &amp;=&amp; \\frac{\\partial S}{\\partial a} + \\frac{\\partial S}{\\partial b} \\frac{db}{da} \\\\<br \/>\n&amp;=&amp; b + a \\cdot (-1) \\\\<br \/>\n&amp;=&amp; b &#8211; a = 0 \\\\<br \/>\n\\therefore\\ \\ a &amp;=&amp; b = \\frac{L}{4}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u306e\u3068\u304d\uff0c\u3059\u306a\u308f\u3061\u6b63\u65b9\u5f62\u306e\u3068\u304d\u3067\u3042\u308b\u3002\u3053\u306e\u3068\u304d\u304c\u6975\u5927\uff08\u6700\u5927\uff09\u3068\u306a\u308b\u3053\u3068\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{d^2 S}{da^2} &amp;=&amp; \\frac{\\partial}{\\partial a} \\frac{dS}{da} + \\frac{db}{da} \\frac{\\partial}{\\partial b}\\frac{dS}{da} \\\\<br \/>\n&amp;=&amp; -1 -1 &lt; 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u4e0a\u306b\u51f8\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u308f\u304b\u308b\u3002<\/p>\n<h3>\u672c\u984c\uff1a\u6955\u5186\u306e\u5468\u9577\u3092\u4e00\u5b9a\u306b\u3057\u305f\u3068\u304d\uff0c\u9762\u7a4d\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\uff1f<\/h3>\n<p>\u4e0a\u8a18\u306e\u7df4\u7fd2\u554f\u984c\u306e\u3088\u3046\u306b\uff0c\u6955\u5186\u306e\u5834\u5408\u3082\u3084\u3063\u3066\u3044\u3051\u3070\u3088\u3044\u304c\uff0c\u6955\u5186\u306e\u5468\u9577\u306f\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u306a\u3044\u305f\u3081\uff0c\u6b21\u5584\u306e\u7b56\u3068\u3057\u3066\uff0c\u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306b\u3088\u308b\u6955\u5186\u5468\u306e\u8fd1\u4f3c\u5f0f\u3092\u4f7f\u3063\u3066\uff0c\u8fd1\u4f3c\u7684\u306b\u8a3c\u660e\u3057\u3066\u307f\u308b\u3002\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3082\u53c2\u8003\u306b\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e7%a9%8d%e5%88%86%ef%bc%9a%e3%81%84%e3%81%8f%e3%81%a4%e3%81%8b%e3%81%ae%e5%bf%9c%e7%94%a8\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e3%81%a7%e6%a5%95%e5%86%86%e3%81%ae%e9%9d%a2%e7%a9%8d%e3%83%bb%e5%91%a8%ef%bc%8c%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%81%ae%e8%a1%a8%e9%9d%a2%e7%a9%8d\/#i-2\">\u53c2\u8003\uff1aMaxima \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6463\/\">\u6955\u5186\u306e\u5468\u306e\u9577\u3055\u306e\u8fd1\u4f3c\u5f0f<\/a><\/li>\n<\/ul>\n<h4>\u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306b\u3088\u308b\u6955\u5186\u306e\u5468\u9577\u306e\u8fd1\u4f3c\u5f0f<\/h4>\n<p>\u9577\u534a\u5f84 $a$\uff0c\u77ed\u534a\u5f84 $b$ \u306e\u6955\u5186\u306e\u5468\u9577\u3092\u3042\u3089\u308f\u3059\u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306b\u3088\u308b\u8fd1\u4f3c\u5f0f\u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nL &amp;\\equiv&amp; \\pi \\left(3 (a+b) \u2013 \\sqrt{(a+3b)(3a+b)} \\right) \\\\<br \/>\n&amp;=&amp; \\pi \\left(3 (a+b) \u2013 \\sqrt{3 a^2 + 10 ab + 3 b^2} \\right)<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3067\u3042\u308a\uff0c\u6955\u5186\u306e\u9762\u7a4d $S$ \u306f<\/p>\n<p>$$S = \\pi a b$$<\/p>\n<p>\u6955\u5186\u306e\u5468\u9577 $L$ \u3092\u4e00\u5b9a\u306b\u4fdd\u3063\u305f\u307e\u307e $a, b$ \u3092\u5909\u5316\u3055\u305b\u308b\u3068\uff0c\u9762\u7a4d $S$ \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $a = b$ \u306e\u5186\u306e\u3068\u304d\u3067\u3042\u308b\u3053\u3068\u3092\uff0c\u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306b\u3088\u308b\u5468\u9577\u306e\u8fd1\u4f3c\u5f0f\u3092\u4f7f\u3063\u3066\u793a\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6530\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/daen1.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<p>\u307e\u305a\uff0c$L = \\mbox{const.} \\equiv L_0$\u00a0 \u3067\u3042\u308b\u306e\u3067\uff0c$a, b$ \u306f\u3069\u3061\u3089\u3082\u72ec\u7acb\u306a\u5909\u6570\u3068\u3044\u3046\u308f\u3051\u306b\u306f\u3044\u304b\u306a\u304f\u306a\u308a\uff0c$b$ \u306f $a$ \u306e\u95a2\u6570 $b = b(a)$ \u3068\u306a\u308b\u3002\u9670\u95a2\u6570\u5b9a\u7406\u3092\u4f7f\u3063\u3066\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{db}{da} &amp;=&amp; &#8211; \\frac{\\frac{\\partial L}{\\partial a}}{\\frac{\\partial L}{\\partial b}} \\\\<br \/>\n&amp;=&amp; &#8211; \\frac{3 &#8211; \\frac{3 a + 5 b}{\\sqrt{3 a^2 + 10 ab + 3 b^2} }}{3 &#8211; \\frac{3 b + 5 a}{\\sqrt{3 a^2 + 10 ab + 3 b^2} }}\\\\<br \/>\n&amp;=&amp; -\\frac{3 \\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211; 3 a &#8211; 5 b}{3 \\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211; 3 b &#8211; 5 a}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u6761\u4ef6\u306e\u3082\u3068\u3067\uff0c$S$ \u304c\u6975\u5024\uff08\u6700\u5927\u5024\uff09\u3092\u6301\u3064\u306e\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\n\\frac{dS}{da} &amp;=&amp; \\frac{\\partial S}{\\partial a} + \\frac{\\partial S}{\\partial b} \\frac{db}{da} \\\\<br \/>\n&amp;=&amp; \\pi b + \\pi a \\cdot\\left(-\\frac{3 \\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211; 3 a &#8211; 5 b}{3 \\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211; 3 b &#8211; 5 a} \\right)\\\\<br \/>\n&amp;=&amp; 3 \\pi (b &#8211; a) \\frac{\\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211;\u00a0 b &#8211;\u00a0 a}{3 \\sqrt{3 a^2 + 10 ab + 3 b^2} &#8211; 3 b &#8211; 5 a} \\\\<br \/>\n&amp;=&amp; 0 \\\\<br \/>\n\\therefore\\ \\ a &amp;=&amp; b<br \/>\n\\end{eqnarray}<\/p>\n<p>\u306e\u3068\u304d\uff0c\u3059\u306a\u308f\u3061\u5186\u306e\u3068\u304d\u3067\u3042\u308b\u3002\u3053\u306e\u3068\u304d\u304c\u6975\u5927\uff08\u6700\u5927\uff09\u3067\u3042\u308b\u3053\u3068\u306f\uff0c$\\displaystyle \\frac{d^2 S}{da^2}$ \u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u9762\u5012\u306a\u306e\u3067\uff0c$\\displaystyle \\frac{dS}{da}$ \u306e\u7b26\u53f7\u304c $(b-a)$ \u3060\u3051\u3067\u6c7a\u307e\u308b\u3053\u3068\u304b\u3089\u308f\u304b\u308b\u3002\uff08\u306a\u305c\u304b\u306f\u5404\u81ea\u8003\u3048\u3066\u307f\u3066\u3002\uff09<\/p>\n<p>\u9762\u7a4d $S$ \u3092 $a$ \u306e\u95a2\u6570 $S(a)$ \u3068\u3057\u3066\uff0c<\/p>\n<ul>\n<li>$a &lt; b$ \u306e\u3068\u304d\uff0c$\\displaystyle \\frac{dS}{da} \\propto (b-a) &gt; 0$\uff0c<\/li>\n<li>$a = b$ \u306e\u3068\u304d\uff0c$\\displaystyle \\frac{dS}{da} \\propto (b-a) = 0$\uff0c<\/li>\n<li>$a &gt; b$ \u306e\u3068\u304d\uff0c$\\displaystyle \\frac{dS}{da} \\propto (b-a) &lt; 0$\uff0c<\/li>\n<\/ul>\n<p>\u3068\u306a\u308a\uff0c$a=b$ \u306e\u3068\u304d\u304c\u6975\u5927\uff08\u6700\u5927\uff09\u3068\u306a\u308b\u3002<\/p>\n<h4>\u95a2\u5b5d\u548c\u306b\u3088\u308b\u6955\u5186\u306e\u5468\u9577\u306e\u8fd1\u4f3c\u5f0f<\/h4>\n<p>\u540c\u69d8\u306a\u3053\u3068\u306f\uff0c\u95a2\u5b5d\u548c\u306b\u3088\u308b\u6955\u5186\u5468\u9577\u306e\u8fd1\u4f3c\u5f0f<\/p>\n<p>\\begin{eqnarray}L_{\\rm Seki} &amp;=&amp; 2 \\sqrt{4 (a-b)^2 + \\pi^2 a b}\\end{eqnarray}<\/p>\n<p>\u3092\u4f7f\u3063\u3066\u3082\u8fd1\u4f3c\u7684\u306b\u8a3c\u660e\u3067\u304d\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9670\u95a2\u6570\u5b9a\u7406\u306e\u7df4\u7fd2\u554f\u984c\u3068\u3057\u3066\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6535\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[21],"tags":[],"class_list":["post-6535","post","type-post","status-publish","format-standard","hentry","category-21","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6535","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=6535"}],"version-history":[{"count":27,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6535\/revisions"}],"predecessor-version":[{"id":6564,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6535\/revisions\/6564"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=6535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=6535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=6535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}