[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21683#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21683","headline":"Brachistochrone  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Brachistochrone  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u8155gistochron\u306e\u8cdb\u7f8e – \u66f2\u7dda\u4e0a\u306e\u3042\u3089\u3086\u308b\u51fa\u767a\u70b9\u304b\u3089\u3001\u30dc\u30fc\u30eb\u306f\u540c\u6642\u306b\u300c\u30b4\u30fc\u30eb\u300d\u306b\u5230\u9054\u3057\u307e\u3059\u3002 Brachistochrone \uff08gr\u3002 \u30d6\u30e9\u30ad\u30b9\u30c8\u30b9 \u6700\u77ed\u3001 \u30af\u30ed\u30ce\u30b9 \u6642\u9593\uff09\u306f\u3001\u521d\u671f\u30dd\u30a4\u30f3\u30c8\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306e\u9593\u306e\u5217\u8eca\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u540c\u69d8\u306b\u9ad8\u304f\u3066\u3082\u4f4e\u3044\u5217\u8eca\u3067\u3042\u308a\u3001\u91cd\u529b\u5f37\u5ea6\u306e\u5f71\u97ff\u306e\u4e0b\u3067\u901f\u5ea6\u3067\u901f\u5ea6\u3067\u59cb\u307e\u308b\u8cea\u91cf\u79fb\u52d5\u306e\u8cea\u91cf\u30dd\u30a4\u30f3\u30c8\u304c\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u307e\u3067\u8fc5\u901f\u306b\u6ed1\u8d70\u3057\u307e\u3059\u3002\u30c8\u30e9\u30c3\u30af\u306e\u6700\u3082\u6df1\u3044\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u3088\u308a\u3082\u6df1\u304f\u306a\u308a\u307e\u3059\u3002 after-content-x4 \u305f\u3068\u3048\u3070\u3001\u305f\u3068\u3048\u3070\u3001\u3088\u308a\u77ed\u3044\u5834\u5408\u3067\u3082\u3001\u30dc\u30c7\u30a3\u306f\u305d\u306e\u3088\u3046\u306a\u30c8\u30e9\u30c3\u30af\u3088\u308a\u3082\u901f\u304f\u30b9\u30e9\u30a4\u30c9\u3057\u307e\u3059\u3002 \u540c\u6642\u306b\u3001\u3053\u306e\u66f2\u7dda\u306f\u30bf\u30c8\u30af\u30ed\u30f3\u3001\u3064\u307e\u308aH.\u66f2\u7dda\u4e0a\u306e\u3059\u3079\u3066\u306e\u51fa\u767a\u70b9\u304b\u3089\u3001\u30de\u30b9\u30dd\u30a4\u30f3\u30c8\u306f\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306b\u5230\u9054\u3059\u308b\u306e\u306b\u540c\u3058\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u4e8b\u5b9f\u306f\u3001\u632f\u308a\u5b50\u306e\u8cea\u91cf\u304c\u30bf\u30c8\u30af\u30ed\u30f3\u3067\u63fa\u308c\u3066\u3044\u308b\u3001SO\u304c\u30b3\u30fc\u30eb\u3057\u305f\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u632f\u308a\u5b50\u3067\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002 after-content-x4 \u30d6\u30e9\u30b8\u30b9\u30c8\u30af\u30ed\u30f3\u306f\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u4e00\u90e8\u3067\u3059\u3002 \u30e8\u30cf\u30f3I\u30d9\u30eb\u30cc\u30fc\u30ea\u306f\u3001\u6700\u901f\u306e\u30b1\u30fc\u30b9\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3057\u307e\u3057\u305f\u3002 1696\u5e74\u3001\u5f7c\u306f\u6700\u7d42\u7684\u306b\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30f3\u3067\u89e3\u6c7a\u7b56\u3092\u898b\u3064\u3051\u307e\u3057\u305f\u3002 [\u521d\u3081] \u4eca\u65e5\u3001\u3042\u306a\u305f\u306f\u3057\u3070\u3057\u3070\u3053\u308c\u3092\u5909\u52d5\u8a08\u7b97\u306e\u8a95\u751f\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 1673\u5e74\u3001Christiaan","datePublished":"2023-12-07","dateModified":"2023-12-07","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e2\/Brachistochronerutschbahn.jpg\/314px-Brachistochronerutschbahn.jpg","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e2\/Brachistochronerutschbahn.jpg\/314px-Brachistochronerutschbahn.jpg","height":"169","width":"314"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21683","wordCount":7896,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4   \u8155gistochron\u306e\u8cdb\u7f8e – \u66f2\u7dda\u4e0a\u306e\u3042\u3089\u3086\u308b\u51fa\u767a\u70b9\u304b\u3089\u3001\u30dc\u30fc\u30eb\u306f\u540c\u6642\u306b\u300c\u30b4\u30fc\u30eb\u300d\u306b\u5230\u9054\u3057\u307e\u3059\u3002  Brachistochrone \uff08gr\u3002 \u30d6\u30e9\u30ad\u30b9\u30c8\u30b9 \u6700\u77ed\u3001 \u30af\u30ed\u30ce\u30b9 \u6642\u9593\uff09\u306f\u3001\u521d\u671f\u30dd\u30a4\u30f3\u30c8\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306e\u9593\u306e\u5217\u8eca\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u540c\u69d8\u306b\u9ad8\u304f\u3066\u3082\u4f4e\u3044\u5217\u8eca\u3067\u3042\u308a\u3001\u91cd\u529b\u5f37\u5ea6\u306e\u5f71\u97ff\u306e\u4e0b\u3067\u901f\u5ea6\u3067\u901f\u5ea6\u3067\u59cb\u307e\u308b\u8cea\u91cf\u79fb\u52d5\u306e\u8cea\u91cf\u30dd\u30a4\u30f3\u30c8\u304c\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u307e\u3067\u8fc5\u901f\u306b\u6ed1\u8d70\u3057\u307e\u3059\u3002\u30c8\u30e9\u30c3\u30af\u306e\u6700\u3082\u6df1\u3044\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u3088\u308a\u3082\u6df1\u304f\u306a\u308a\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u305f\u3068\u3048\u3070\u3001\u305f\u3068\u3048\u3070\u3001\u3088\u308a\u77ed\u3044\u5834\u5408\u3067\u3082\u3001\u30dc\u30c7\u30a3\u306f\u305d\u306e\u3088\u3046\u306a\u30c8\u30e9\u30c3\u30af\u3088\u308a\u3082\u901f\u304f\u30b9\u30e9\u30a4\u30c9\u3057\u307e\u3059\u3002 \u540c\u6642\u306b\u3001\u3053\u306e\u66f2\u7dda\u306f\u30bf\u30c8\u30af\u30ed\u30f3\u3001\u3064\u307e\u308aH.\u66f2\u7dda\u4e0a\u306e\u3059\u3079\u3066\u306e\u51fa\u767a\u70b9\u304b\u3089\u3001\u30de\u30b9\u30dd\u30a4\u30f3\u30c8\u306f\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306b\u5230\u9054\u3059\u308b\u306e\u306b\u540c\u3058\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u4e8b\u5b9f\u306f\u3001\u632f\u308a\u5b50\u306e\u8cea\u91cf\u304c\u30bf\u30c8\u30af\u30ed\u30f3\u3067\u63fa\u308c\u3066\u3044\u308b\u3001SO\u304c\u30b3\u30fc\u30eb\u3057\u305f\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u632f\u308a\u5b50\u3067\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d6\u30e9\u30b8\u30b9\u30c8\u30af\u30ed\u30f3\u306f\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u4e00\u90e8\u3067\u3059\u3002 \u30e8\u30cf\u30f3I\u30d9\u30eb\u30cc\u30fc\u30ea\u306f\u3001\u6700\u901f\u306e\u30b1\u30fc\u30b9\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3057\u307e\u3057\u305f\u3002 1696\u5e74\u3001\u5f7c\u306f\u6700\u7d42\u7684\u306b\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30f3\u3067\u89e3\u6c7a\u7b56\u3092\u898b\u3064\u3051\u307e\u3057\u305f\u3002 [\u521d\u3081] \u4eca\u65e5\u3001\u3042\u306a\u305f\u306f\u3057\u3070\u3057\u3070\u3053\u308c\u3092\u5909\u52d5\u8a08\u7b97\u306e\u8a95\u751f\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 1673\u5e74\u3001Christiaan Huygens\u306f\u3001\u5f7c\u306e\u8ad6\u6587\u30db\u30ed\u30ed\u30b8\u30a6\u30e0\u30aa\u30b7\u30e9\u30c8\u30ea\u30a6\u30e0\u306b\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u632f\u308a\u5b50\u3092\u542b\u3080\u30ae\u30a2\u306e\u5bdb\u5927\u306a\u632f\u308a\u5b50\u6642\u8a08\u3092\u767a\u8868\u3057\u307e\u3057\u305f\u3002\u5f7c\u306f\u3001\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u81ea\u4f53\u306e\u9032\u5316\u304c\u518d\u3073\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u5229\u7528\u3057\u307e\u3057\u305f\u3002\u305f\u3060\u3057\u3001\u30ae\u30a2\u306e\u7cbe\u5ea6\u306e\u5229\u70b9\u306f\u3001\u6469\u64e6\u306e\u5897\u52a0\u306b\u88dc\u308f\u308c\u3066\u3044\u307e\u3059\u3002 Brachistochron\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3067\u8aac\u660e\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30dd\u30a4\u30f3\u30c8\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3067\u5909\u5316\u3055\u305b\u308b\u30ed\u30fc\u30ab\u30eb\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u89d2\u5ea6\u306e\u95a2\u6570\u3068\u3057\u3066        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d5\u30a1\u30a4 {displaystyle varphi} \uff08\u30a2\u30fc\u30c1\u30b5\u30a4\u30ba\uff09\u3001\u305d\u306e\u5468\u308a\u306b\u534a\u5f84\u306e\u30db\u30a4\u30fc\u30eb\u304c\u3042\u308a\u307e\u3059 r {displaystyle r} \u30ed\u30fc\u30eb\u30aa\u30d5\u3059\u308b\u3068\u304d\u3001\u5f7c\u3089\u306f\u305d\u3046\u3067\u3059 \u30d0\u30c4 {displaystyle x} – \u3068 \u3068 {displaystyle y} -Coodinates\uff1a \u30d0\u30c4 = r de \uff08 \u30d5\u30a1\u30a4  –  \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3001 {displaystyle x = rcdot\uff08varphi -sin varphi\uff09,,} \u3068 = r de \uff08  –  \u521d\u3081 + cos \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3002 {displaystyle y = rcdot\uff08-1+cos varphi\uff09\u3001\u3002} \u3053\u306e\u66f2\u7dda\u3092\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002\u89d2\u5ea6\u306e\u534a\u5f84\u300c\u5730\u533a\u30bb\u30f3\u30bf\u30fc\u306e\u63a5\u89e6\u70b9\u3092\u53d6\u308b\u300d\u306f\u3001\u3059\u3067\u306b\u5c55\u958b\u3055\u308c\u3066\u3044\u308b\u30eb\u30fc\u30c8\u3067\u3059\u3002 \u3067\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046 \u30d0\u30c4 {displaystyle x}  –  \u3068 {displaystyle y}  – \u66f2\u7dda\u3092\u30d9\u30a4\u30f3\u3057\u307e\u3059 \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y\uff08x\uff09} \u3001\u305d\u308c\u306b\u6cbf\u3063\u3066\u3001\u6700\u521d\u304b\u3089\u30de\u30b9\u304c\u30dd\u30a4\u30f3\u30c8\u3057\u307e\u3059 \uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 0 \u3001 0 \uff09\uff09 {displaystyle\uff08x\u3001y\uff09=\uff080,0\uff09} \u7d99\u7d9a\u7684\u306a\u6642\u9593\u3067 t {displaystylet} \u76ee\u6a19\u306b \uff08 \u30d0\u30c4 \u00af \u3001 \u3068 \u00af \uff09\uff09 {displaystyle\uff08{overline {x}}\u3001{overline {y}}\uff09} \u30b9\u30e9\u30a4\u30c7\u30a3\u30f3\u30b0\u3002 \u5f7c\u306f\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6301\u3063\u3066\u3044\u307e\u3059 \u3068 kin= 12m \u306e 2= 12m \uff08 vx2+ vy2\uff09\uff09 = 12m \uff08 (dxdt)2+(dydxdxdt)2\uff09\uff09 = 12m (dxdt)2\uff08 1+(dydx)2\uff09\uff09 {displaystyle e_ {text {kin}} = {frac {1} {2}}\u3001m\u3001v^{2} = {frac {1} {2}}\u3001m\u3001\uff08{v_ {x}}}^{2}+{b_ {{2ac} {} {} {} {} {} {} {{2} {{2} {{2} {{2} {{2} {{2} {{2} {{2} {} {2}\u5de6\uff08\u5de6\uff08\u5de6\uff08{frac {mathrm {d} x} {mathrm {d} t}\u53f3\uff09^{2}+\u5de6\uff08{frac {mathrm {d} y} {mathrm {d} x}}\u3001{frac = {d} x} {{mathrm {{d} {d} {d} {d} {d} {d} {frac {1} {2}}\u3001m\u3001left\uff08{frac {mathrm {d} x} {mathrm {d} t}}\u53f3\uff09^{2}\u5de6\uff081+\u5de6\uff08{frac {mathrm {d} y} {d} x} {2\uff09^{2\uff09 \u305d\u3057\u3066\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc \u3068 pot= m de g de \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle e_ {text {pot}} = mcdot gcdot y\uff08x\uff09} \u3042\u308b \u3068 {displaystyle y} \u91cd\u529b\u5834\u306e\u9ad8\u3055\u3068 g {displaystyle g} \u91cd\u5ea6\u306e\u52a0\u901f\u3002 \u6700\u521d\u306b\u8d77\u6e90\u304b\u3089\u5206\u96e2\u3055\u308c\u305f\u4f11\u7720\u91cf\u306e\u8cea\u91cf\u304c\u3042\u308b\u5834\u5408\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u5168\u4f53\u304c\u5217\u8eca\u306b\u6cbf\u3063\u3066\u4fdd\u5b58\u3055\u308c\u3001\u521d\u671f\u5024\u30bc\u30ed\u304c\u3042\u308a\u307e\u3059\u3002 0 = 12m (dxdt)2\uff08 1+(dydx)2\uff09\uff09 + m de g de \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle 0 = {frac {1} {2}}\u3001m\u3001\u5de6\uff08{frac {mathrm {d} x} {mathrm {d} t}}\u53f3\uff09^{2}\u30c9\u30c3\u30c8Y\uff08x\uff09} \u3053\u308c\u306f\u5f8c\u306b\u3067\u304d\u307e\u3059 dxdt{display style {twomanc {pushm {d} x} {mhrmm {d} t}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} \u6eb6\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u53cd\u8ee2\u95a2\u6570\u306e\u5c0e\u51fa\u3001 t \uff08 \u30d0\u30c4 \uff09\uff09 {displaystylet\uff08x\uff09} \u305d\u308c\u306f\u3001\u7c92\u5b50\u304c\u305d\u306e\u5834\u6240\u3092\u4f55\u6642\u306b\u6307\u5b9a\u3057\u307e\u3059 \uff08 \u30d0\u30c4 \u3001 \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 \uff09\uff09 {displaystyle\uff08x\u3001y\uff08x\uff09\uff09} \u901a\u308a\u629c\u3051\u3066\u3001\u3053\u308c\u306b\u9006\u3067\u3059 dtdx= 1+(dydx)2\u22122gy{displaystyle {frac {mathrm {d} t} {mathrm {d} x}} = {sqrt {frac {frac {mathrm {d} y} {mathrm {d} x}}\uff09^{2} {-2\u3001g\u3001g\u3001g\u3001g\u3001 \u3092\u901a\u3057\u3066\u7d71\u5408\u3057\u307e\u3059 \u30d0\u30c4 {displaystyle x} -0\u304b\u3089\u30a8\u30ea\u30a2 \u30d0\u30c4 \u00af {displaystyle {overline {x}}} \u3001\u3053\u308c\u306b\u3088\u308a\u3001\u7528\u8a9e\u304c\u6700\u5c0f\u5316\u3055\u308c\u307e\u3059 t {displaystylet} \u30ec\u30fc\u30eb\u66f2\u7dda\u306e\u6a5f\u80fd\u3068\u3057\u3066 \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y\uff08x\uff09}  t [ \u3068 ] = 12g\u222b 0x\u00af1+(dydx)2\u2212yd \u30d0\u30c4 {displaystyle t [y] = {frac {1} {sqrt {2\u3001g}}} int _ {0}^{overline {x}}\u3001{sqrt {frac {frac {1+\uff08{frac {mathrm {d} y} {{d} {d}}}}}} {} {{d}} } mathrm {d} x} \u7269\u7406\u7684\u5909\u52d5\u306e\u554f\u984c\u3067\u4e00\u822c\u7684\u306a\u540d\u524d\u306b\u63a5\u7d9a\u3059\u308b\u305f\u3081\u306b\u3001\u7d71\u5408\u5909\u6570\u3092\u547c\u3073\u51fa\u3057\u307e\u3059 t {displaystylet} \u3001 \u8aac\u660e  –  \u3068 {displaystyle -y} \u3068 r {displaystyle r} \u305d\u3057\u3066\u3001\u5358\u306b\u305d\u308c\u3092\u6700\u5c0f\u5316\u3057\u307e\u3059 2 g {displaystyle {sqrt {2\u3001g}}} \u6a5f\u80fd\u7684\u306b\u5897\u6b96\u3057\u307e\u3057\u305f\u3002\u305d\u306e\u305f\u3081\u3001\u52b9\u679c\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u307e\u3059 \u306e [ r ] = \u222b 1+(drdt)2rd t {displaystyle w [r] = int\u3001{sqrt {frac {1+\uff08{frac {d} r} {mathrm {d} t}}\uff09^{2}} {r}}} mathrm {d} t}} \u30e9\u30b0\u30e9\u30f3\u30b4\u30eb\u30c8\u95a2\u6570\u3092\u4f7f\u7528 L\uff08 t \u3001 r \u3001 \u306e \uff09\uff09 = 1+v2r{displaystyle {mathcal {l}}\uff08t\u3001r\u3001v\uff09= {sqrt {frac {1+v^{2}} {r}}}}}} \u30e9\u30b0\u30e9\u30f3\u95a2\u6570\u306f\u7d71\u5408\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304b\u3089\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u6642\u9593 t {displaystylet} \u4f9d\u5b58\u3057\u307e\u3059\u3001\u30a8\u30fc\u30c6\u30eb\u5b9a\u7406\u306b\u5f93\u3063\u3066\u95a2\u9023\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc \/\u30cf\u30df\u30eb\u30c8\u30f3\u95a2\u6570 h = \u306e \u2202 vL –  L=  –  1r(1+v2){displaystyle h = vpartial _ {v} {mathcal {l}}  –  {mathcal {l}} =  –  {frac {1} {sqrt {r\uff081+v^{2}\uff09}}}}}} \u8ecc\u9053\u306b\u4e57\u3063\u3066 r \uff08 t \uff09\uff09 {displaystyle r\uff08t\uff09} \u306e\u305f\u3081\u306b\u4fdd\u5b58\u3055\u308c\u3066\u3044\u307e\u3059 \u306e [ r ] {displaystyle w [r]} \u6700\u5c0f\u9650\u306b\u306a\u308a\u307e\u3059\u3002\u95a2\u6570 r \uff08 t \uff09\uff09 {displaystyle r\uff08t\uff09} \u6b63\u306e\u5b9a\u6570\u3067\u6e80\u305f\u3055\u308c\u307e\u3057\u305f r {displaystyle r} \u65b9\u7a0b\u5f0f \uff08 1+(drdt)2\uff09\uff09 r = 2 r {displaystyle\u5de6\uff081+\u5de6\uff08{frac {mathrm {d} r} {mathrm {d} t}}\u53f3\uff09^{2}\u53f3\uff09\u3001r = 2\u3001r} \u307e\u305f (drdt)2 –  2Rr=  –  \u521d\u3081 {displaystyle left\uff08{frac {mathrm {d} r} {mathrm {d} t}}\u53f3\uff09^{2}  –  {frac {2\u3001r} {r}} = -1} \u30b1\u30d7\u30e9\u30fc\u306e\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306b\u3042\u308b\u7c92\u5b50\u306e\u3088\u3046\u306b \u221d  –  \u521d\u3081 \/ r {disclayStyle\u63d0\u6848-1 \/ r} \u30b5\u30df\u30c3\u30c8\u306e\u9ad8\u3055\u304b\u3089\u5782\u76f4 2 r {displaystyle 2\u3001r} \u6edd\u3002 \u5225\u3005\u306e\u5909\u66f4\u53ef\u80fd\u306a\u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u4ee3\u308f\u308a\u306b drdt{displaystyle {tfrac {mathrm {d} r} {mathrm {d} t}}}}} \u6eb6\u89e3\u3057\u3066\u7d71\u5408\u3059\u308b\u305f\u3081\u306b\u3001\u305d\u308c\u3092\u78ba\u8a8d\u3059\u308b\u3060\u3051\u3067\u3059 t \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = r \uff08 \u30d5\u30a1\u30a4  –  \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3001  r \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = r \uff08 \u521d\u3081  –  cos \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle T\uff08varphi\uff09= r\u3001\uff08varphi -sin varphi\uff09\u3001r\uff08varphi\uff09= r\u3001\uff081 -Cos varphi\uff09} \u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u89e3\u3067\u3042\u308a\u3001\u305d\u308c\u306b\u3088\u3063\u3066 drdt= drd\u03c6dtd\u03c6= sin\u2061\u03c61\u2212cos\u2061\u03c6{displaystyle {mathrm {d}}} {d}} {d}} = {mathrm {d} r} varphi}} {mathrm {d} varphi}}}}}}} {frac {sin varphi} {1-cos}}}}}}}} \u60aa\u7528\u3055\u308c\u305f\u3002\u3060\u304b\u3089\u3042\u306a\u305f\u304c\u63a2\u3057\u3066\u3044\u308b\u96fb\u8eca\u306f\u305d\u3046\u3067\u3059 \uff08 \u30d0\u30c4 \u3001 \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 \uff09\uff09 {displaystyle\uff08x\u3001y\uff08x\uff09\uff09} \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af (x(\u03c6)y(\u03c6))= r (\u03c6\u2212sin\u2061\u03c6cos\u2061\u03c6\u22121)= r (\u03c6\u22121)+ (cos\u2061\u03c6\u2212sin\u2061\u03c6sin\u2061\u03c6cos\u2061\u03c6)(0R){displaystyle {begin {pmatrix} x\uff08varphi\uff09rix} varphi \\ -1end {pmatrix}}+{begin {pmatrix} cos varphi\uff06-sin varphi \\ sin varphi\uff06cos varphi end end end \u6700\u5f8c\u306e\u5206\u89e3\u304b\u3089\u3001\u5217\u8eca\u304c \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y\uff08x\uff09} \u304b\u3089\u629c\u3051\u51fa\u3057\u307e\u3059\u30ed\u30fc\u30ab\u30eb\u30d9\u30af\u30bf\u30fc r \uff08 \u30d5\u30a1\u30a4 \u3001  –  \u521d\u3081 \uff09\uff09 {displaystyle R\u3001\uff08varphi\u3001-1\uff09} \u534a\u5f84\u306e\u3042\u308b\u30db\u30a4\u30fc\u30eb\u306e\u30cf\u30d6 r {displaystyle r} \u4e0b\u306b\u307e\u3068\u3081\u307e\u3059 \u30d0\u30c4 {displaystyle x}  – \u30ed\u30fc\u30eb\u30b9\u306b\u52a0\u3048\u3066\u3001\u6700\u521d\u306b\u4e0a\u5411\u304d\u306b\u4e0a\u5411\u304d\u306b\u89d2\u5ea6\u3067\u6307\u3059\u97f3\u30d9\u30af\u30bf\u30fc \u30d5\u30a1\u30a4 {displaystyle varphi} \u56de\u8ee2\u3057\u307e\u3059\u3002\u66f2\u7dda\u306f\u3001\u30ed\u30fc\u30ea\u30f3\u30b0\u30db\u30a4\u30fc\u30eb\u306e\u5468\u8fba\u70b9\u306e\u7d4c\u8def\u3067\u3059\u3002 \u9244\u9053\u306f\u3001\u4f53\u306e\u8cea\u91cf\u3068\u91cd\u91cf\u3001\u3064\u307e\u308a\u5730\u4e0b\u52a0\u901f\u306e\u30b5\u30a4\u30ba\u306b\u95a2\u4fc2\u306a\u304f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002 \u540c\u69d8\u306b\u3001\u30ed\u30fc\u30bf\u30ea\u30fc\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u5438\u53ce\u3059\u308b\u30ed\u30fc\u30ea\u30f3\u30b0\u30dc\u30fc\u30eb\u3082\u3001\u7406\u60f3\u7684\u306a\u66f2\u7dda\u306b\u306f\u4f55\u3082\u5909\u308f\u308a\u307e\u305b\u3093\u3002 \u6700\u521d\u306e\u63a5\u7dda\u306f\u5782\u76f4\u3067\u3059\u3002 2\u3064\u306eBrachistochrons\u304c\u958b\u59cb\u70b9\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306e\u9593\u306b\u540c\u3058\u52fe\u914d\u3092\u6301\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3089\u306f\u4f3c\u3066\u3044\u307e\u3059\u3002 \u52fe\u914d\u304c2\/\u03c0\uff0863.66\uff05\uff09\u4ee5\u4e0a\u3067\u3042\u308b\u5834\u5408\u3001\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306f\u66f2\u7dda\u306e\u6700\u3082\u6df1\u3044\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308a\u3001\u30b0\u30ec\u30fc\u30c9\u304c\u5c0f\u3055\u3044\u5834\u5408\u3001\u4f4e\u3044\u70b9\u306f\u958b\u59cb\u70b9\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u306e\u9593\u306b\u3042\u308a\u307e\u3059\u3002 \u52fe\u914d\u304c0\u306e\u5834\u5408\u3001\u958b\u59cb\u70b9\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u304c\u540c\u3058\u9ad8\u3055\u306e\u5834\u5408\u3001\u66f2\u7dda\u306f\u5bfe\u79f0\u7684\u3067\u3059\u3002 \u7b2c1\u30d5\u30a7\u30fc\u30ba\uff1a\u4e21\u65b9\u306e\u30dc\u30fc\u30eb\u304c\u30d1\u30fc\u306b\u3042\u308a\u307e\u3059\u3002 2\u756a\u76ee\u306e\u30d5\u30a7\u30fc\u30ba\uff1a\u30d5\u30ed\u30f3\u30c8\u30dc\u30fc\u30eb\u306f\u3088\u308a\u5f37\u3044\u52fe\u914d\u306b\u3088\u3063\u3066\u52a0\u901f\u3057\u307e\u3059\u3002 3\u756a\u76ee\u306e\u30d5\u30a7\u30fc\u30ba\uff1a\u30d5\u30ed\u30f3\u30c8\u30dc\u30fc\u30eb\u306f\u9577\u3044\u65b9\u6cd5\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u30d5\u30ed\u30f3\u30c8\u306b\u3042\u308a\u307e\u3059\u3002 \u2191  Acta\u306f\u5b66\u3093\u3060\u3002 \uff081696\uff09\u3002 Siehe IstvanSzab\u00f3\uff1a \u6a5f\u68b0\u7684\u539f\u5247\u306e\u6b74\u53f2\u3002 3\u756a\u76ee\u306e\u4fee\u6b63\u304a\u3088\u3073\u62e1\u5f35\u72481987\u3001p\u3002110\u3001ISBN 978-3-0348-9980-2\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21683#breadcrumbitem","name":"Brachistochrone  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]