{"id":2569,"date":"2022-03-25T17:48:39","date_gmt":"2022-03-25T08:48:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2569"},"modified":"2025-07-09T09:51:36","modified_gmt":"2025-07-09T00:51:36","slug":"%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e8%a1%a8%e8%a8%98%e6%b3%95%e3%81%a8%e6%bc%94%e7%ae%97","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e8%a1%a8%e8%a8%98%e6%b3%95%e3%81%a8%e6%bc%94%e7%ae%97\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u306e\u8868\u8a18\u6cd5"},"content":{"rendered":"<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u3068\u306f\uff0c\u5927\u304d\u3055\u3068\u5411\u304d\u3092\u6301\u3064\u91cf\u3067\u3042\u308b\u30023\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u30d9\u30af\u30c8\u30eb\u306f\uff0c3\u672c\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3068\u6210\u5206\uff08\u305d\u308c\u305e\u308c\u306e\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306b\u305d\u3063\u305f\u9577\u3055\uff09\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u3067\u306f\uff0c3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u8868\u3057\u65b9\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u308b\u3002<br \/>\n<!--more--><\/p>\n<h3 id=\"yui_3_17_2_1_1648197625746_1397\">3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u8868\u3057\u65b9<\/h3>\n<ul id=\"yui_3_17_2_1_1648197625746_1396\">\n<li id=\"yui_3_17_2_1_1648197625746_1395\">\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u7cfb\uff08\\(xyz\\)- \u7cfb\uff09\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u57fa\u672c\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\boldsymbol{i}, \\,\\boldsymbol{j},\\, \\boldsymbol{k}\\) \u3068<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6210\u5206<\/strong><\/span> \\( a_x, \\,a_y, \\,a_z \\) \u3092\u4f7f\u3063\u3066\uff0c$$ \\boldsymbol{a} = a_x \\,\\boldsymbol{i} + a_y \\,\\boldsymbol{j} + a_z \\,\\boldsymbol{k}$$<br \/>\n\u3053\u306e\u66f8\u304d\u65b9\u304c\u6700\u3082\u6b63\u5f0f\u306a\u8868\u8a18\u6cd5\u3002<br \/>\n\u306a\u304a\uff0c\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{e}_x,\u00a0 \\boldsymbol{e}_y, \\boldsymbol{e}_z\\) \u3068\u66f8\u3044\u305f\u308a\uff0c\\(\\boldsymbol{e}_1,\u00a0 \\boldsymbol{e}_2, \\boldsymbol{e}_3\\) \u306a\u3069\u3068\u66f8\u3044\u305f\u308a\u3059\u308b\u5834\u5408\u3082\u3042\u308b\u3002<\/p>\n<ul id=\"yui_3_17_2_1_1648197625746_1396\">\n<li>\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{e}_x,\u00a0 \\boldsymbol{e}_y, \\boldsymbol{e}_z\\) \u3068\u66f8\u304f\u5834\u5408\u306f\uff0c<br \/>\n$$\\boldsymbol{a} = a_x \\,\\boldsymbol{e}_x + a_y \\,\\boldsymbol{e}_y + a_z \\,\\boldsymbol{e}_z $$<\/li>\n<li>\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{e}_1,\u00a0 \\boldsymbol{e}_2, \\boldsymbol{e}_3\\) \u3068\u66f8\u304f\u5834\u5408\u306f\uff0c\u3055\u3089\u306b\u6210\u5206\u3082 \\(a_x \\Rightarrow a^1, \\ a_y \\Rightarrow a^2, \\ a_z \\Rightarrow a^3\\) \u306e\u3088\u3046\u306b\u66f8\u3044\u3066<br \/>\n\\begin{eqnarray}<br \/>\n\\boldsymbol{a} &amp;=&amp; a^1\\, \\boldsymbol{e}_1 + a^2\\, \\boldsymbol{e}_2 + a^3\\, \\boldsymbol{e}_3 \\\\<br \/>\n&amp;=&amp; \\sum_{i=1}^3 \\, a^i \\, \\boldsymbol{e}_i<br \/>\n\\end{eqnarray}<br \/>\n\u7279\u306b\uff0c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{r}\\) \u306f<br \/>\n\\begin{eqnarray}<br \/>\n\\boldsymbol{r} &amp;=&amp; x^1\\, \\boldsymbol{e}_1 + x^2\\, \\boldsymbol{e}_2 + x^3\\, \\boldsymbol{e}_3 \\\\<br \/>\n&amp;=&amp; \\sum_{i=1}^3 \\, x^i \\, \\boldsymbol{e}_i<br \/>\n\\end{eqnarray}<br \/>\n1\u756a\u76ee\u306e\u5ea7\u6a19\uff0c2\u756a\u76ee\u306e\u5ea7\u6a19\uff0c3\u756a\u76ee\u306e\u5ea7\u6a19\u3068\u3044\u3046\u610f\u5473\u3067<br \/>\n$$x \\Rightarrow x^1, \\\u00a0 y \\Rightarrow x^2, \\\u00a0 z \\Rightarrow x^3$$<br \/>\n\u3068\u66f8\u3044\u3066\u3044\u308b\u306e\u3067\u3042\u3063\u3066\uff0c\u6c7a\u3057\u3066 $x$ \u306e2\u4e57\u3068\u304b3\u4e57\u3068\u304b\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u3067\u306f\u306a\u3044\uff0c\u5ff5\u306e\u305f\u3081\u3002<br \/>\n\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u306e\u6dfb\u5b57\u3092\u4e0a\u4ed8\u304d\u306b\u3059\u308b\u3068\uff0c\u3053\u306e\u3088\u3046\u306b\u7d2f\u4e57\u3068\u6df7\u540c\u3059\u308b\u306e\u3067\u307e\u304e\u3089\u308f\u3057\u3044\u3068\u601d\u3046\u304b\u3082\u3057\u308c\u306a\u3044\u304c\uff0c\u3057\u304b\u3057\uff0c\u5c06\u6765\uff0c\u4e00\u822c\u76f8\u5bfe\u8ad6\u3068\u304b\u3092\u5b66\u3076\u3088\u3046\u306b\u306a\u308b\u3068\uff0c\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u306f\u4e0a\u4ed8\u304d\u6dfb\u5b57\uff0c\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u306f\u4e0b\u4ed8\u304d\u6dfb\u5b57<\/strong><\/span>\u300d\u3068\u3044\u3046\u8a18\u6cd5\u304c\u5927\u5909\u4fbf\u5229\u306b\u306a\u308b\u3093\u3067\u3059\u3088\uff08<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%81%ae%e8%a6%8f%e7%b4%84%e3%81%a8%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%86%85%e7%a9%8d\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u3053\u306e\u3078\u3093<\/strong><\/span><\/a>\u3068\u304b\u3092\u53c2\u7167\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u7279\u306b\uff0c\u5168\u3066\u306e\u6210\u5206\u304c\u30bc\u30ed\u3067\u3042\u308b\u30d9\u30af\u30c8\u30eb\u3092\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30bc\u30ed\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u300d\u3068\u547c\u3073\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u3089\u3057\u304f\u300c\u6570\u5f0f\u30d5\u30a9\u30f3\u30c8\u306e\u592a\u5b57\u300d\u3067 \\(\\boldsymbol{0}\\) \u3068\u66f8\u304f\u3002<br \/>\n$$\\boldsymbol{0} = 0\\, \\boldsymbol{i} + 0\\, \\boldsymbol{j} + 0\\, \\boldsymbol{k}$$<br \/>\n<span style=\"font-family: helvetica, arial, sans-serif; color: #ff0000;\"><strong>\u30b9\u30ab\u30e9\u30fc\uff08\u6570\u5024\uff09\u3068\u3057\u3066\u306e\u30bc\u30ed $0$\u00a0 \u3068\uff0c\u30bc\u30ed\u30d9\u30af\u30c8\u30eb $\\boldsymbol{0}$ \u306f\u5fc5\u305a\u533a\u5225\u3067\u304d\u308b\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\uff01<\/strong><\/span><\/li>\n<li>\u7dda\u5f62\u4ee3\u6570\u5b66\u3067\u306f\uff0c\u30d9\u30af\u30c8\u30eb\u3068\u8a00\u3048\u3070\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5217\u30d9\u30af\u30c8\u30eb<\/strong><\/span>\u300d\uff08\u6210\u5206\u3092\u7e26\u306b\u306a\u3089\u3079\u305f\u3082\u306e\uff09\u306e\u3053\u3068\u3002<br \/>\n$$\\boldsymbol{a} = \\left(<br \/>\n\\begin{array}{c}<br \/>\na_x \\\\<br \/>\na_y \\\\<br \/>\na_z<br \/>\n\\end{array}<br \/>\n\\right)$$<br \/>\n\u5217\u30d9\u30af\u30c8\u30eb\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u8ee2\u7f6e<\/strong><\/span>\u3092\u3068\u3063\u305f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u884c\u30d9\u30af\u30c8\u30eb<\/strong><\/span> $ \\boldsymbol{a}^T = (a_x\\ \\ a_y\\ \\ a_z) $ \u3082\u3042\u308b\u304c\uff0c\u6210\u5206\u306e\u9593\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b9\u30da\u30fc\u30b9\u3067\u533a\u5207\u308b<\/strong><\/span>\u3002<br \/>\n\u3055\u3089\u306b\u8a00\u3048\u3070\uff0c\\(xyz\\)-\u7cfb\u3067\u306a\u304f\u3066\u3082\u3088\u304f\uff0c\u6210\u5206\u306e\u6570\u30823\u3064\u3060\u3051\u3067\u3042\u308b\u5fc5\u8981\u3082\u306a\u3044\u306e\u3067 $n$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u8868\u793a\u306f\uff0c<br \/>\n$$\\boldsymbol{a} = \\left(<br \/>\n\\begin{array}{c}<br \/>\na_1 \\\\<br \/>\na_2 \\\\<br \/>\n\\vdots \\\\<br \/>\na_n<br \/>\n\\end{array}<br \/>\n\\right)$$<\/li>\n<li>\u529b\u5b66\uff0c\u96fb\u78c1\u6c17\u5b66\u7b49\u3067\u306f\uff0c\u3044\u3061\u3044\u3061\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3092\u66f8\u304b\u305a\u306b<br \/>\n$$ \\boldsymbol{a} = (a_x, \\ a_y, \\ a_z) $$ \u3068<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6210\u5206\u306e\u9593\u3092\u30ab\u30f3\u30de <\/strong>$(,)$<strong> \u3067\u533a\u5207\u3063\u3066\u6a2a\u306b\u4e26\u3079\u308b<\/strong><\/span>\u3002<\/li>\n<\/ul>\n<h3>\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u8868\u8a18\uff0c\u30ab\u30f3\u30de\u3067\u533a\u5207\u308b\uff1f\u533a\u5207\u3089\u306a\u3044\uff1f<\/h3>\n<p>$$ \\boldsymbol{a} = (a_x, \\ a_y, \\ a_z) $$ \u3068\u8868\u8a18\u3059\u308b\u5834\u5408\u3068\uff0c<br \/>\n$$\\boldsymbol{a} = \\left(<br \/>\n\\begin{array}{c}<br \/>\na_x \\\\<br \/>\na_y \\\\<br \/>\na_z<br \/>\n\\end{array}<br \/>\n\\right)$$<\/p>\n<p>\u307e\u305f\u306f<br \/>\n$$ \\boldsymbol{a}^T = (a_x\\ \\ a_y\\ \\ a_z) $$<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ab\u30f3\u30de\u3067\u533a\u5207\u308c\u3070\u3044\u3044\u306e\uff1f\u533a\u5207\u3089\u306a\u304f\u3066\u3082\u3044\u3044\u306e\uff1f\u3069\u3063\u3061\uff1f\uff1f<\/strong><\/span> &#8230; \u3068\u60a9\u3080\u4eba\u306e\u305f\u3081\u306b\u3002<\/p>\n<p>\u3042\u304f\u307e\u3067\u3082\u6b63\u5f0f\u306a\u6210\u5206\u8868\u8a18\u6cd5\u306f\uff0c\u300c\u5217\u30d9\u30af\u30c8\u30eb\u300d\uff08\u6210\u5206\u3092\u7e26\u306b\u306a\u3089\u3079\u305f\u3082\u306e\uff09\u3067\u3042\u308a\uff0c<\/p>\n<p>$$\\boldsymbol{a} = \\left(<br \/>\n\\begin{array}{c}<br \/>\na_x \\\\<br \/>\na_y \\\\<br \/>\na_z<br \/>\n\\end{array}<br \/>\n\\right)$$<\/p>\n<p>\u3067\u3082\uff0c\u3053\u308c\u3060\u3068\u30b9\u30da\u30fc\u30b9\u3092\u6d88\u8cbb\u3059\u308b\u306e\u3067\uff0c<\/p>\n<p>$$ \\boldsymbol{a} = (a_x, \\ a_y, \\ a_z) $$<\/p>\n<p>\u3068\u66f8\u3044\u3066\uff0c$a_x$ \u306e\u3042\u3068\u306e<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ab\u30f3\u30de<\/strong>$(,) $<strong> \u306f\u5b9f\u306f\u6539\u884c\u3057\u3066\u6b21\u306e\u884c\u3092\u8868\u3059\u3093\u3060\uff0c\u3068\u7406\u89e3\u3059\u308b<\/strong><\/span>\u3002\u307e\u305f $a_y$ \u306e\u3042\u3068\u306e\u30ab\u30f3\u30de $(,) $ \u3082\u5b9f\u306f\u3055\u3089\u306b\u6539\u884c\u3057\u3066\u6b21\u306e\u884c\u3092\u8868\u3059\u3093\u3060\u3068\u7406\u89e3\u3059\u308c\u3070\uff0c$\\boldsymbol{a} = (a_x, \\ a_y, \\ a_z) $ \u306f\u7d50\u5c40<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>3\u884c\u306b\u308f\u305f\u308b\u6210\u5206\u8868\u8a18\u30921\u884c\u306b\u307e\u3068\u3081\u3066\u7bc0\u7d04\u8868\u793a\u3059\u308b\u65b9\u6cd5\u3067\u3042\u308b<\/strong><\/span>\uff0c\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u601d\u3048\u3070\uff0c\u6210\u5206\u306e\u9593\u3092\u30b9\u30da\u30fc\u30b9\u306e\u307f\u306b\u3059\u308b\u304b\uff0c\u30ab\u30f3\u30de\u3067\u533a\u5207\u308b\u304b\uff0c\u3068\u3044\u3046\u7570\u306a\u3063\u305f\u8868\u8a18\u6cd5\u3068\u6298\u308a\u5408\u3044\u3092\u3064\u3051\u3066\u751f\u304d\u3066\u3044\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u601d\u3046\u304c\uff0c\u3044\u304b\u304c\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2586 size-medium\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec001-300x156.png\" alt=\"\" width=\"300\" height=\"156\" 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