[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22892#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22892","headline":"Eulersche Winkel -Wikipedia","name":"Eulersche Winkel -Wikipedia","description":"before-content-x4 3\u3064\u306e\u500b\u3005\u306e\u500b\u5225\u304c\u4f53\u306e\u8ef8z\u3001x ‘\u3001z “\u306e\u56de\u8ee2\u306e\u7d50\u679c\u3068\u3057\u3066\u4f53\u3092\u56de\u3059\u3002 \u72ec\u81ea\u306e\u5ea7\u6a19\u7cfb\uff1a \u8150\u6557 \u4fee\u6b63\u3055\u308c\u305f\u53c2\u7167\u30b7\u30b9\u30c6\u30e0\uff1a \u9752 Eulerschen Winkel \uff08\u307e\u305f \u30aa\u30a4\u30e9\u30fc\u30b7\u30e7\u30c3\u30d7 \uff09\u3001\u30b9\u30a4\u30b9\u306e\u6570\u5b66\u8005\u3067\u3042\u308b\u30ec\u30aa\u30f3\u30cf\u30eb\u30c8\u30fb\u30aa\u30a4\u30e9\u30fc\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u306e\u306f\u30013\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9818\u57df\u306e\u56fa\u4f53\u4f53\u306e\u65b9\u5411\uff08\u56de\u8ee2\uff09\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b3\u3064\u306e\u89d2\u5ea6\u306e\u6587\u3067\u3059\u3002 [\u521d\u3081] \u3042\u306a\u305f\u306f\u901a\u5e38\u4e00\u7dd2\u306b\u3044\u307e\u3059 a \u3001 b \u3001 c","datePublished":"2023-12-03","dateModified":"2023-12-03","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/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\/8\/85\/Euler2a.gif\/220px-Euler2a.gif","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/85\/Euler2a.gif\/220px-Euler2a.gif","height":"208","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22892","wordCount":29962,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 3\u3064\u306e\u500b\u3005\u306e\u500b\u5225\u304c\u4f53\u306e\u8ef8z\u3001x ‘\u3001z “\u306e\u56de\u8ee2\u306e\u7d50\u679c\u3068\u3057\u3066\u4f53\u3092\u56de\u3059\u3002 \u72ec\u81ea\u306e\u5ea7\u6a19\u7cfb\uff1a \u8150\u6557 \u4fee\u6b63\u3055\u308c\u305f\u53c2\u7167\u30b7\u30b9\u30c6\u30e0\uff1a \u9752  Eulerschen Winkel \uff08\u307e\u305f \u30aa\u30a4\u30e9\u30fc\u30b7\u30e7\u30c3\u30d7 \uff09\u3001\u30b9\u30a4\u30b9\u306e\u6570\u5b66\u8005\u3067\u3042\u308b\u30ec\u30aa\u30f3\u30cf\u30eb\u30c8\u30fb\u30aa\u30a4\u30e9\u30fc\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u306e\u306f\u30013\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9818\u57df\u306e\u56fa\u4f53\u4f53\u306e\u65b9\u5411\uff08\u56de\u8ee2\uff09\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b3\u3064\u306e\u89d2\u5ea6\u306e\u6587\u3067\u3059\u3002 [\u521d\u3081] 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[4]  \u5e97 p {displaystyle p} \u3001 Q {displaystyle q} \u3001 r {displaystyle r} \u4ed5\u4e8b\u304b\u3089 [5] \u30aa\u30a4\u30e9\u30fc\u306b\u3088\u3063\u3066 3\u5206\u306e1\u3067\u3001\u90f5\u4fbf\u5c40\u6240\u306e\u307f\u304c\u516c\u958b\u3055\u308c\u3066\u3044\u307e\u3059 [5] \u5f7c\u306f\u3064\u3044\u306b3\u3064\u306e\u89d2\u5ea6\u3092\u7387\u3044\u307e\u3057\u305f p {displaystyle p} \u3001 Q {displaystyle q} \u3068 r {displaystyle r} \u5f7c\u304c\u30dc\u30c7\u30a3\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\u306e\u5b87\u5b99\u8010\u6027\u5ea7\u6a19\u3078\u306e\u5909\u9769\u3092\u8aac\u660e\u3057\u3001\u305d\u308c\u304c\u4eca\u65e5\u5f7c\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u89d2\u5ea6\u306b\u4e00\u81f4\u3059\u308b\u3082\u306e\u3092\u8aac\u660e\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u5f7c\u306e\u624b\u9806\u306f\u3001\u4eca\u65e5\u306e\u73fe\u5728\u306e\u624b\u9806\u3068\u306f\u5927\u304d\u304f\u7570\u306a\u308a\u30011\u3064\u306e\u5ea7\u6a19\u7cfb\u304c3\u3064\u306e\u9023\u7d9a\u3057\u305f\u5ea7\u6a19\u8ef8\u306e\u5468\u308a\u3067\u4ed6\u306e\u5ea7\u6a19\u7cfb\u306b\u8ee2\u9001\u3055\u308c\u307e\u3059\u3002\u6700\u521d\u306e\u4f5c\u54c1\u306b\u4f3c\u305f\u30aa\u30a4\u30e9\u30fc\u306e\u8b70\u8ad6\u3067\u3059\u304c\u3001\u3088\u308a\u5b89\u4fa1\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u306a\u308a\u307e\u3059 [5] \uff1as\u3002 50 3\u3064\u306e\u89d2\u5ea6\u3067 p {displaystyle p} \u3001 Q {displaystyle q} \u3068 r {displaystyle r} \u306a\u305c\u306a\u3089\u3001\u3053\u3053 – \u73fe\u4ee3\u306e\u8a71\u3059\u65b9\u6cd5\u3067 – \u5f7c\u306f\u7dda\u306e\u6b63\u898f\u6027\u3060\u3051\u3067\u306a\u304f\u3001\u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u5217\u306e\u5217\u306e\u305d\u308c\u3082\u4f7f\u7528\u3057\u3066\u3044\u305f\u304b\u3089\u3067\u3059\u3002\u5f7c\u3089\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u610f\u5473\u3092\u660e\u78ba\u306b\u3059\u308b\u305f\u3081\u306b\u3001\u5f7c\u306f\u4ea4\u5dee\u70b9\u3092\u898b\u307e\u3057\u305f a {displaystyle a} \u3001 b {displaystyle b} \u3001 c {displaystyle c} \u30e6\u30cb\u30c3\u30c8\u30dc\u30fc\u30eb\u3068\u5bfe\u5fdc\u3059\u308b\u4ea4\u5dee\u70b9\u3092\u5099\u3048\u305f\u7a7a\u9593\u8010\u6027\u5ea7\u6a19\u7cfb\u306e a {displaystyle a} \u3001 b {displaystyle b} \u3001 c {displaystyle c} \u4f53\u306e\u9577\u3055\u306e\u30b7\u30b9\u30c6\u30e0\u3068\u30a2\u30fc\u30c1\u306e\u30b3\u30b7\u30cc\u30b9\u304c a a {displaystyle aa} \u3001 a b {displaystyle ab} \u3001…\u3001 c c {displaystyle cc} \u5909\u63db\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u306f\u6b63\u78ba\u3067\u3059\u3002\u3060\u304b\u3089\u305d\u3046\u3067\u3059 p = a a {displaystyle p = aa} \u9593\u306e\u89d2\u5ea6 \u30d0\u30c4 {displaystyle x} – \u305d\u3057\u3066\u305d\u306e \u30d0\u30c4 {displaystyle x} -\u8ef8\u3002\u3055\u3089\u306b\u3001\u7403\u72b6\u306e\u4e09\u89d2\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059 Q {displaystyle q} \u89d2\u5ea6 a {displaystyle a} \u30dc\u30fc\u30eb\u30c8\u30e9\u30a4\u30a2\u30f3\u30b0\u30eb\u3067 a b a {displaystyle aba} \u3068 r {displaystyle r} \u89d2\u5ea6 a {displaystyle a} \u30dc\u30fc\u30eb\u30c8\u30e9\u30a4\u30a2\u30f3\u30b0\u30eb\u3067 a b a {displaystyle aba} \u306f\u3002\u4eca\u65e5\u3001\u5bfe\u5fdc\u3059\u308b\u89d2\u5ea6\u306f\u305d\u3046\u3067\u306f\u3042\u308a\u307e\u305b\u3093 \u30d0\u30c4 \u30d0\u30c4 {displaystyle xx}  – \u30ec\u30d9\u30eb\u3067\u3059\u304c\u3001\u7d50\u3073\u76ee\u304b\u3089\u305d\u308c\u307e\u3067 n {displaystyle n} \u6e2c\u5b9a; X-Y-X\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u4eca\u65e5\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b\u30d5\u30af\u30ed\u30a6\u306e\u89d2\u5ea6\u3068\u306e\u63a5\u7d9a\u306f\u3001 a = r + 90 \u2218 {displaystyle alpha = r+90^{circ}} \u3001 b = p {displaystyle beta = p} \u3068 c =  –  Q + 90 \u2218 {displaystyle gamma = -q+90^{circ}} \u3002 \u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306f1788\u5e74\u306b\u6301\u3061\u8fbc\u307e\u308c\u307e\u3057\u305f \u5206\u6790\u529b\u5b66 [6] \u5909\u63db\u65b9\u7a0b\u5f0f\u306e2\u3064\u306e\u6d3e\u751f\u3002\u6700\u521d [6] \uff1as\u3002 381\u2013388 \u89d2\u5ea6\u306e\u540d\u524d\u3092\u9664\u3044\u3066\u6b63\u3057\u3044\uff08\u5f7c\u3089\u306f\u305d\u308c\u3092\u547c\u3070\u308c\u3066\u3044\u308b l = p {displaystyle lambda = p} \u3001 m = r {displaystyle mu = r} \u3068 n = Q {displaystyle nu = q} \uff09\u672c\u8cea\u7684\u306b\u30aa\u30a4\u30e9\u30fc\u306e\u3082\u306e\u3002\u4e8c\u756a\u76ee [6] \uff1as\u3002 398\u2013401 Z-X-Z\u30b7\u30fc\u30b1\u30f3\u30b9-Again\u306e\u6700\u65b0\u306e\u8a73\u7d30\u306a\u8868\u73fe\u3068\u4ed6\u306e\u89d2\u5ea6\u540d\u3068\u4e00\u81f4\u3057\u307e\u3059\uff08 \u30d5\u30a1\u30a4 = c {displaystyle varphi = gamma} \u3001 \u03c6 = a {displaystyle psi = alpha} \u3001 \u304a\u304a = b {displaystyle omega = beta} \uff09\u3002  \u5ea7\u6a19\u5909\u63db\u3001\u6a19\u6e96X\u6761\u7d04\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u30b7\u30fc\u30b1\u30f3\u30b9 \u9752 \uff1a\u958b\u59cb\u70b9\u306e\u5ea7\u6a19\u7cfb \u7dd1 \uff1aXY\u30ec\u30d9\u30eb\u306e\u307e\u3063\u3059\u3050\u3001X\u8ef8\u306e\u4e2d\u9593\u5c64\u3092\u307e\u3063\u3059\u3050\u306b\u5207\u308b \u8150\u6557 \uff1a\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u5ea7\u6a19\u7cfb \u4ee5\u4e0b\u3067\u306f\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u306b\u96a3\u63a5\u3059\u308b\u3088\u3046\u306b\u3001\u5c0f\u3055\u306a\u6587\u5b57\u304c\u4ed8\u3044\u305f\u958b\u59cb\u70b9\uff08\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30d6\u30eb\u30fc\uff09\u306e\u5ea7\u6a19\u7cfb\u306e\u8ef8\u306f \u30d0\u30c4 {displaystyle x} \u3001 \u3068 {displaystyle y} \u3068 \u3068 {displaystyle with} \u3001\u5bfe\u5fdc\u3059\u308b\u5927\u6587\u5b57\u3092\u6301\u3064\u30bf\u30fc\u30b2\u30c3\u30c8\uff08\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30ec\u30c3\u30c9\uff09\u306e\u8ef8 \u30d0\u30c4 {displaystyle x} \u3001 \u3068 {displaystyle y} \u3068 \u3068 {displaystyle with} \u5c02\u7528\u3002 Table of Contents\u5e7e\u4f55\u5b66\u7684\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u672c\u8cea\u7684\u306a\u56de\u8ee2\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5916\u56e0\u6027\u56de\u8ee2\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d5\u30a3\u30ae\u30e5\u30a2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff08\u30a2\u30af\u30c6\u30a3\u30d6\u56de\u8ee2\uff09 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] TransformationSmatrix [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5927\u4f1a [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ed\u30fc\u30eb\u3001\u30cb\u30c3\u30af\u3001\u8caa\u6b32\u306a\u89d2\u5ea6\uff1az-ys-x\u2033\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] TransformationSmatrizen [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u4f8b [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5e7e\u4f55\u5b66\u7684\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u30d0\u30c4 {displaystyle x}  –  \u3068 {displaystyle y} \u30ec\u30d9\u30eb\u3068 \u30d0\u30c4 {displaystyle x}  –  \u3068 {displaystyle y}  – \u76f4\u7dda\u3067\u30d9\u30a4\u30f3\u30ab\u30c3\u30c8 n {displaystyle n} \uff08\u30ce\u30c3\u30c8\u30e9\u30a4\u30f3\uff09\u3002\u3053\u308c\u306f\u5782\u76f4\u306b\u3042\u308a\u307e\u3059 \u3068 {displaystyle with} -axse and on \u3068 {displaystyle with} -\u8ef8\u3002 \u3053\u3053\u3067\u8aac\u660e\u3059\u308b\u30aa\u30a4\u30e9\u30fc\u89d2\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3002 a {displaystyle alpha} \u306e \u30d0\u30c4 {displaystyle x}  – \u30ce\u30c3\u30c8\u30e9\u30a4\u30f3\u3068\u89d2\u5ea6\u306b\u5230\u9054\u3057\u307e\u3059 c {displaystyle\u30ac\u30f3\u30de} \u30ce\u30fc\u30c9\u30e9\u30a4\u30f3\u304b\u3089 \u30d0\u30c4 {displaystyle x} -een\u8ef8\u306f\u305d\u308c\u3068\u547c\u3070\u308c\u307e\u3059 \u6a19\u6e96-X\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3 \u3002\u3057\u305f\u304c\u3063\u3066\u3001 \u6a19\u6e96-Y\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3 \u306e\u89d2\u5ea6 \u3068 {displaystyle y}  – \u30ce\u30c3\u30c8\u30e9\u30a4\u30f3\u304b\u3089\u30ce\u30fc\u30c9\u30e9\u30a4\u30f3\u304b\u3089\u306e\u8ef8 \u3068 {displaystyle y} -een\u6e2c\u5b9a\u3002 \u6a19\u6e96X\u898f\u5247\u306f\u901a\u5e38\u3001\u53e4\u5178\u7269\u7406\u5b66\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u306e\u4ee3\u308f\u308a\u306b a {displaystyle alpha} \u3001 b {displaystyle\u30d9\u30fc\u30bf} \u3068 c {displaystyle\u30ac\u30f3\u30de} \u901a\u5e38\u3001\u89d2\u5ea6\u306f\u3042\u308a\u307e\u3059 \u30d5\u30a1\u30a4 {displaystyle varphi} \u3001 th {displaystyletheta} \u3068 \u03c6 {displaystyle psi} \u5c02\u7528\u3002\u4e00\u65b9\u3001\u91cf\u5b50\u529b\u5b66\u3067\u306f\u3001\u6a19\u6e96I\u6761\u7d04\u304c\u512a\u5148\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7279\u306b\u3001SO3\u30ed\u30fc\u30bf\u30ea\u30fc\u30b0\u30eb\u30fc\u30d7\u306e\u8868\u73fe\u306f\u3001\u3044\u308f\u3086\u308b\u30a6\u30a3\u30b0\u30ca\u30fcD\u30de\u30c8\u30ea\u30c3\u30af\u306b\u3088\u3063\u3066\u305d\u308c\u306b\u5fdc\u3058\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u672c\u8cea\u7684\u306a\u56de\u8ee2\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u56de\u8ee2 r {displaystyle r} \u3001\u305d\u308c\u306f\u305d\u308c\u3067\u3059 \u30d0\u30c4 \u3068 \u3068 {displaystyle xyz}  – \u305d\u306e\u4e2d\u306e\u30b7\u30b9\u30c6\u30e0 \u30d0\u30c4 \u3068 \u3068 {displaystyle xyz}  – \u30b7\u30b9\u30c6\u30e0\u30bf\u30fc\u30f3\u306f\u30013\u3064\u306e\u56de\u8ee2\u306b\u5206\u5272\u3067\u304d\u307e\u3059\u3002\u6a19\u6e96X\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u308c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u3053\u306e\u30bf\u30fc\u30f3\u3067\u306f\u3001\u65b0\u3057\u3044\u5ea7\u6a19\u7cfb\u304c\u9023\u7d9a\u3057\u3066\u4f5c\u6210\u3055\u308c\u307e\u3059\u3002 \u56de\u8ee2 n {displaystyle n} \u5468\u308a\u306e\u56de\u8ee2\u3082\u540c\u69d8\u3067\u3059 \u30d0\u30c4 ‘ {displaystyle x ‘}  – \u5230\u9054\u3001\u5468\u308a\u306e\u56de\u8ee2 \u3068 {displaystyle with}  – \u5468\u308a\u306e\u56de\u8ee2\u3092\u7372\u5f97\u3057\u307e\u3059 \u3068 \u300c {disspastyle with ”} -\u8ef8\u3002\u5168\u4f53\u7684\u306a\u30bf\u30fc\u30f3 r {displaystyle r} \u3057\u305f\u304c\u3063\u3066\u3001\u30bf\u30fc\u30f3\u304b\u3089\u51fa\u307e\u3059 r \u3068 \uff08 a \uff09\uff09 {displaystyle r_ {z}\uff08alpha\uff09} \u3001 r x\u2032\uff08 b \uff09\uff09 {displaystyle r_ {x ‘}\uff08beta\uff09} \u3068 r z\u2033\uff08 c \uff09\uff09 {displaystyle r_ {z ”}\uff08\u30ac\u30f3\u30de\uff09} \u4e00\u7dd2\uff1a r = r z\u2033\uff08 c \uff09\uff09 \u2218 r x\u2032\uff08 b \uff09\uff09 \u2218 r z\uff08 a \uff09\uff09 {displaystyle r = r_ {z ”}\uff08gamma\uff09circ r_ {x ‘}\uff08beta\uff09circ r_ {z}\uff08alpha\uff09} \u3057\u305f\u304c\u3063\u3066\u3001\u56de\u8ee2\u8ef8\u306e\u9806\u5e8f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u3068 {displaystyle with} -ACHS\u2192 \u30d0\u30c4 ‘ {displaystyle x ‘} -ACHS\u2192 \u3068 \u300c {disspastyle with ”}  – \u8ef8\u307e\u305f\u306f\u77ed\u3044 \u3068 {displaystyle with}  –  \u30d0\u30c4 ‘ {displaystyle x ‘}  –  \u3068 \u300c {disspastyle with ”} \u3002 \u56de\u8ee2\u306e\u3053\u306e\u3088\u3046\u306a\u5206\u89e3\u306f\u3001\u305d\u308c\u305e\u308c\u304c\u5ea7\u6a19\u8ef8\u306e\u5468\u308a\u3067\u56de\u8ee2\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u547c\u3070\u308c\u307e\u3059\u3002 \u672c\u8cea\u7684 \u30bb\u30c3\u30c8\u30cb\u30f3\u30b0\u30b7\u30fc\u30b1\u30f3\u30b9\u3002 \u5916\u56e0\u6027\u56de\u8ee2\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u540c\u3058\u56de\u8ee2 r {displaystyle r} \u307e\u305f\u3001\u5143\u306e\u5ea7\u6a19\u8ef8\u30923\u3064\u306e\u500b\u5225\u306e\u30bf\u30fc\u30f3\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u89d2\u5ea6\u306f\u540c\u3058\u307e\u307e\u3067\u3059\u304c\u3001\u30bf\u30fc\u30f3\u306e\u9806\u5e8f\u306f\u56de\u8ee2\u3057\u3001\u4e2d\u9593\u5c64 \u30d0\u30c4 ‘ \u3068 ‘ \u3068 ‘ {displaystyle x’y’z ‘} \u3068 \u30d0\u30c4 \u300c \u3068 \u300c \u3068 \u300c {displaystyle x”y”z ”} \u56fa\u6709\u306e\u56de\u8ee2\u3068\u306f\u7570\u306a\u308a\u307e\u3059\uff1a\u6700\u521d\u306b\u4f53\u306f\u89d2\u5ea6\u306e\u5468\u308a\u306b\u306a\u308a\u307e\u3059 c {displaystyle\u30ac\u30f3\u30de} \u306b \u3068 {displaystyle with} -een\u8ef8\u3001\u305d\u306e\u5f8c b {displaystyle\u30d9\u30fc\u30bf} \u306b \u30d0\u30c4 {displaystyle x} -axse\uff08\u9593\u306e\u89d2\u5ea6 \u30d0\u30c4 {displaystyle x} – \u3068 \u30d0\u30c4 \u300c {displaystyle x ”} -een\u306f\u9593\u3067\u305d\u308c\u3068\u540c\u3058\u3067\u3059 \u30d0\u30c4 {displaystyle x} – \u305d\u3057\u3066\u305d\u306e \u30d0\u30c4 ‘ {displaystyle x ‘} -axse\u3001\u3059\u306a\u308f\u3061 c {displaystyle\u30ac\u30f3\u30de} \uff09\u305d\u3057\u3066\u6700\u5f8c\u306b\u89d2\u5ea6\u306e\u5468\u308a a {displaystyle alpha} \u306b \u3068 {displaystyle with} -axse\uff08\u305d\u308c\u306f\u305d\u3046\u306a\u308b\u3067\u3057\u3087\u3046 \u30d0\u30c4 {displaystyle x}  – \u7d50\u3073\u76ee\u306e\u8ef8 n {displaystyle n} \u56de\u8ee2\u3057\u3001\u305d\u306e\u9593\u306e\u89d2\u5ea6 n {displaystyle n} \u305d\u3057\u3066\u305d\u306e \u30d0\u30c4 {displaystyle x} -ACHS\u3067\u3059 c {displaystyle\u30ac\u30f3\u30de} \uff09\u3002\u4ee3\u6570\u7684\u6b63\u5f53\u5316\u306f\u3001\u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u30d8\u30ea\u30d1\u30eb\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u4e0b\u306b\u3042\u308a\u307e\u3059\u3002\u3060\u304b\u3089\u305d\u3046\u3067\u3059 r = r z\uff08 a \uff09\uff09 \u2218 r x\uff08 b \uff09\uff09 \u2218 r z\uff08 c \uff09\uff09 {displaystyle r = r_ {z}\uff08alpha\uff09circ r_ {x}\uff08beta\uff09circ r_ {z}\uff08gamma\uff09} \u3002 \u5143\u306e\u5ea7\u6a19\u8ef8\u304c\u5e38\u306b\u56de\u8ee2\u3059\u308b\u3088\u3046\u306a\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u547c\u3070\u308c\u307e\u3059 \u5916\u56e0\u6027 \u30bb\u30c3\u30c8\u30cb\u30f3\u30b0\u30b7\u30fc\u30b1\u30f3\u30b9\u3002 \u3057\u305f\u304c\u3063\u3066\u3001\u5185\u56e0\u6027\u304a\u3088\u3073\u5916\u56e0\u6027\u56de\u8ee2\u306e\u8aac\u660e\u306f\u540c\u7b49\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u672c\u8cea\u7684\u306a\u56de\u8ee2\u306e\u8aac\u660e\u306f\u3088\u308a\u8a18\u8ff0\u7684\u3067\u3059\u304c\u3001\u8aac\u660e\u306f\u5916\u56e0\u6027\u56de\u8ee2\u306b\u3088\u3063\u3066\u6570\u5b66\u7684\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3084\u3059\u3044\u3067\u3059\u3002 \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u3088\u308b\u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30aa\u30a4\u30e9\u30fc\u89d2\u306e\u5468\u308a\u306e\u56de\u8ee2\u306f\u3001\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u8aac\u660e\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u30a8\u30f3\u30c8\u30ea\u306f\u3001\u30aa\u30a4\u30e9\u30fc\u30a6\u30a3\u30f3\u30b1\u30eb\u306e\u526f\u9f3b\u8154\u3068\u30b3\u30b5\u30a4\u30f3\u5024\u3067\u3059\u3002\u30a4\u30e1\u30fc\u30b8\u30f3\u30b0\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3068\u5ea7\u6a19\u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u533a\u5225\u3057\u307e\u3059\u3002\u6a19\u6e96X\u898f\u5247\u306e\u3053\u308c\u3089\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002\u6a19\u6e96I\u898f\u5247\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001X\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u306e\u305f\u3081\u306e\u57fa\u672c\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u4ee3\u308f\u308a\u306b\u3001y\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u540c\u69d8\u306b\u5f97\u3089\u308c\u307e\u3059\u3002 \u30d5\u30a3\u30ae\u30e5\u30a2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff08\u30a2\u30af\u30c6\u30a3\u30d6\u56de\u8ee2\uff09 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3067 \u30a2\u30af\u30c6\u30a3\u30d6\u56de\u8ee2 \uff08 \u30a2\u30ea\u30d0\u30a4 \uff09\u90e8\u5c4b\u306e\u30dd\u30a4\u30f3\u30c8\u3068\u30d9\u30af\u30c8\u30eb\u3092\u56de\u3057\u307e\u3059\u3002\u5ea7\u6a19\u7cfb\u304c\u8a18\u9332\u3055\u308c\u307e\u3059\u3002\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9 r {displaystyle r} \u3053\u306e\u56f3\u306e\u753b\u50cf\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3059\u3002\u56de\u8ee2\u3057\u305f\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19 w\u2192= r \uff08 v\u2192\uff09\uff09 {displayStyle {thing {w}} = r\uff08{thing {v}}\uff09} \u5143\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u5ea7\u6a19\u306e\u7d50\u679c v\u2192{displaystyle {thing {v}}} \u30ed\u30fc\u30bf\u30ea\u30fc\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3068\u306e\u4e57\u7b97\u306b\u3088\u308a\uff1a (wxwywz)= r (vxvyvz)\u3002 {displaystyle {begin {pmatrix} w_ {x} \\ w_ {y} \\ w_ {z} \\ end {pmatrix}} = r {begin {pmatrix} v_ {x} \\ v_ {y} \\ v_ {z} {pmatrix}}}}} \u5ea7\u6a19\u8ef8\uff08\u57fa\u672c\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff09\u306e\u5468\u308a\u306e\u56de\u8ee2\u306e\u30a4\u30e1\u30fc\u30b8\u30f3\u30b0\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 r x\uff08 a \uff09\uff09 = (1000cos\u2061\u03b1\u2212sin\u2061\u03b10sin\u2061\u03b1cos\u2061\u03b1)\u3001 r y\uff08 a \uff09\uff09 = (cos\u2061\u03b10sin\u2061\u03b1010\u2212sin\u2061\u03b10cos\u2061\u03b1)\u3001 r z\uff08 a \uff09\uff09 = (cos\u2061\u03b1\u2212sin\u2061\u03b10sin\u2061\u03b1cos\u2061\u03b10001){displaystyle r_ {x}\uff08alpha\uff09= {begin {pmatrix} 1\uff060\uff060 \\ 0\uff06cos alpha\uff06-sin alpha \\ 0\uff06sin alpha\uff06cos alpha end {pmatrix}} Alpha\uff060\uff060\uff06cos alpha end {pmatrix}}\u3001quad r_ {z}\uff08alpha\uff09= {begin {pmatrix} cos alpha\uff06-sin alpha\uff060 \\ sin alpha\uff06cos alpha\uff060 \\ 0\uff060\uff061end {pmatrix}}}} \u89d2\u5ea6\u306e\u5468\u308a\u306e\u56de\u8ee2\u7528 a {displaystyle alpha} \u306b \u30d0\u30c4 {displaystyle x}  – \u305d\u308c\u3092\u7372\u5f97\u3057\u307e\u3059 \u3068 {displaystyle y} -ACHS AND THE \u3068 {displaystyle with} -\u8ef8\u3002 \u8907\u5408\u56de\u8ee2\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u500b\u3005\u306e\u56de\u8ee2\u306e\u884c\u5217\u304b\u3089\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u5897\u6b96\u304b\u3089\u5f97\u3089\u308c\u307e\u3059\u3002\u57fa\u672c\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u5143\u306e\u5ea7\u6a19\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u3092\u8a18\u8ff0\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u5916\u56e0\u6027\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059 r = r z\uff08 a \uff09\uff09 \u2218 r x\uff08 b \uff09\uff09 \u2218 r z\uff08 c \uff09\uff09 {displaystyle r = r_ {z}\uff08alpha\uff09circ r_ {x}\uff08beta\uff09circ r_ {z}\uff08gamma\uff09} \u30a4\u30e9\u30b9\u30c8\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u53d7\u3051\u53d6\u308a\u307e\u3059 Rzxz=Rz(\u03b1)Rx(\u03b2)Rz(\u03b3)=(cos\u2061\u03b1\u2212sin\u2061\u03b10sin\u2061\u03b1cos\u2061\u03b10001)(1000cos\u2061\u03b2\u2212sin\u2061\u03b20sin\u2061\u03b2cos\u2061\u03b2)(cos\u2061\u03b3\u2212sin\u2061\u03b30sin\u2061\u03b3cos\u2061\u03b30001)=(cos\u2061\u03b1cos\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3\u2212cos\u2061\u03b1sin\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3sin\u2061\u03b1sin\u2061\u03b2sin\u2061\u03b1cos\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3\u2212sin\u2061\u03b1sin\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3\u2212cos\u2061\u03b1sin\u2061\u03b2sin\u2061\u03b2sin\u2061\u03b3sin\u2061\u03b2cos\u2061\u03b3cos\u2061\u03b2){displaystyle {begin {aligned} r_ {zxz}\uff06= r_ {z}\uff08alpha\uff09\u3001r_ {x}\uff08beta\uff09\u3001r_ {z}\uff08gamma\uff09\\\uff06= {begin {pmatrix} cos alpha\uff06-sin alpha\uff060 \\ sin alpha\uff06cospha\uff060 \\ 0\uff060 \\ 0\uff060 \\ 0\uff06 {begin {pmatrix} 1\uff060\uff060 \\ 0\uff06cos beta\uff06-sin beta \\ 0\uff06sin beta\uff06cos beta end {pmatrix}}} {begin {pmatrix} cos gamma\uff06-sin\u30ac\u30f3\u30de\uff060 \\ sin\u30ac\u30f3\u30de\uff06cos\u30ac\u30f3\u30de\uff060 \\ -sin alpha cos beta sin gamma\uff06-cos alpha sin gamma -sin alpha cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos beta sin gamma\uff06-sin sin sin sin sin sin sin gamma +cos alpha cos cos cos cos cos cos cos beta beta sin sin sin sin sin sin sin cos cos beta cos beta cos beta\u7d42\u4e86{aligned}}} TransformationSmatrix [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u5143\u306e\uff08\u30b9\u30da\u30fc\u30b9 – \u30d7\u30eb\u30fc\u30d5\uff09\u5ea7\u6a19\u7cfb\u304b\u3089\u30bf\u30fc\u30f3\uff08\u30dc\u30c7\u30a3\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\uff09\u307e\u305f\u306f\u305d\u306e\u9006\u3078\u306e\u5ea7\u6a19\u5909\u63db\u3092\u8a18\u8ff0\u3057\u307e\u3059\u3002\u4f53\u8010\u6027\u5ea7\u6a19\u7cfb\u304b\u3089\u30eb\u30fc\u30e0\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\u3078\u306e\u5ea7\u6a19\u5909\u63db\u306e\u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u4e0a\u8a18\u306e\u30d5\u30a9\u30fc\u30e1\u30fc\u30b7\u30e7\u30f3\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\u9006\u5909\u63db\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u3053\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u8ee2\u7f6e\u3067\u3059\u3002\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059 v\u2192{displaystyle {thing {v}}} \u7a7a\u9593\u8010\u6027\u5ea7\u6a19\u7cfb\u306e\u5ea7\u6a19 \u306e \u30d0\u30c4 \u3001 \u306e \u3068 \u3001 \u306e \u3068 {displaystyle v_ {x}\u3001v_ {y}\u3001v_ {z}} \u305d\u3057\u3066\u3001\u30dc\u30c7\u30a3\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\u306e\u5ea7\u6a19 \u306e \u30d0\u30c4 \u3001 \u306e \u3068 \u3001 \u306e \u3068 {displaystyle v_ {x}\u3001v_ {y}\u3001v_ {z}} \u9069\u7528\u3055\u308c\u307e\u3059 (vxvyvz)=Rzxz(vXvYvZ)=Rz(\u03b1)Rx(\u03b2)Rz(\u03b3)(vXvYvZ)=(cos\u2061\u03b1\u2212sin\u2061\u03b10sin\u2061\u03b1cos\u2061\u03b10001)(1000cos\u2061\u03b2\u2212sin\u2061\u03b20sin\u2061\u03b2cos\u2061\u03b2)(cos\u2061\u03b3\u2212sin\u2061\u03b30sin\u2061\u03b3cos\u2061\u03b30001)(vXvYvZ)=(cos\u2061\u03b1cos\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3\u2212cos\u2061\u03b1sin\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3sin\u2061\u03b1sin\u2061\u03b2sin\u2061\u03b1cos\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3\u2212sin\u2061\u03b1sin\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3\u2212cos\u2061\u03b1sin\u2061\u03b2sin\u2061\u03b2sin\u2061\u03b3sin\u2061\u03b2cos\u2061\u03b3cos\u2061\u03b2)(vXvYvZ){displayStyle {begin {aligned} {begin {pmarix} v_ {x} \\ v_ {y} \\ v_ {y} \\ v_ {z} end {pmatrix} {pmatrix} {begin {pmatrix} v_ {x} \\ v_ {x} \\ v_ {x} {x} {pmatrix} \\\uff06= r_ {z {z}\uff08alpha\uff09\u3001r_x}\uff08be ta\u3001r_ {z}\uff08gamma\uff09{begin {pmatrix} v_ {x} \\ v_ {y} \\ v_ {z} {pmarix} {a a begint} {pmar\uff06= begint {pmarix} {pmar\uff06= begint}\u30a2\u30eb\u30d5\u30a1\uff06 – \u30b7\u30f3\u30a2\u30eb\u30d5\u30a1\uff061PA\uff061p\uff061\uff060\uff060\uff061p\uff061p\uff061p\uff061p\uff061p\uff061pha\uff060\uff060\uff060\uff060\uff060\uff06\uff06cos betta\uff06 –  you beta \\ 0\uff06sin beta\uff06cos beta end {pmatrix}} 0\uff061END {PMATRIX}}} {begin {pmarix} v_ {x} \\ v_ {x} \\ v_ {pmatrix}} \\\uff06= {begintrix}} \\\uff06= {begintrix}} cos cos -sin alpha cos cos beta sin gamma\uff06-cos cos cos cos cos beta beta beta beta beta\u30ac\u30f3\u30de\uff06-sin alpha sin gamma +cos alpha cos beta cos beta cos beta cos beta beta gamma\uff06-cos alpha cos beta cos beta beta end {pmatrix}} {begin {pmatrix} \u3068 (vXvYvZ)=RzxzT(vxvyvz)=Rz(\u03b3)TRx(\u03b2)TRz(\u03b1)T(vxvyvz)=(cos\u2061\u03b3sin\u2061\u03b30\u2212sin\u2061\u03b3cos\u2061\u03b30001)(1000cos\u2061\u03b2sin\u2061\u03b20\u2212sin\u2061\u03b2cos\u2061\u03b2)(cos\u2061\u03b1sin\u2061\u03b10\u2212sin\u2061\u03b1cos\u2061\u03b10001)(vxvyvz)=(cos\u2061\u03b1cos\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3sin\u2061\u03b1cos\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2sin\u2061\u03b3sin\u2061\u03b2sin\u2061\u03b3\u2212cos\u2061\u03b1sin\u2061\u03b3\u2212sin\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3\u2212sin\u2061\u03b1sin\u2061\u03b3+cos\u2061\u03b1cos\u2061\u03b2cos\u2061\u03b3sin\u2061\u03b2cos\u2061\u03b3sin\u2061\u03b1sin\u2061\u03b2\u2212cos\u2061\u03b1sin\u2061\u03b2cos\u2061\u03b2)(vxvyvz).{displaystyle {begin {aligned} {begin {pmarix} v_ {x} \\ v_ {y} \\ v_ {z} end {pmatrix}\uff06= r_ {zxz}^{zxz}^} {begn {begn} v_ {x} {x} \\ v_ {v_ {v_ {v_ {v_ {v^v_ {bign} = r_ {z}\uff08gamma\uff09^^ {gamma\uff09\u3001r_ {x {x}\uff08beta\uff09^{t}\u3001r_ {z}\uff08alpha\uff09^{t} {begin {pmatrix} v_ {x} \\ v_ {x} \\ v_ {pm {{{pM {{z} \\ v_ {z} {pmr {begin {pmatrix} cos\uff06sin gamma\uff060 \\ -sin gamma\uff06cos gamma\uff060\uff061end {pmatrix} {begintrix} {begintrix} {begintrix} 111\uff060\uff060\uff060\uff06cos beta\uff06sin beta \\ 0\uff06-sin beta\uff06cos beta beta beta beta {pmatrix {pmatrix {pppha -sin alpha\uff061p\uff061p\uff061p\uff061p\uff061pud {pmarix}} {beginx}} {pmarix} v_ {x {y} \\ v_ {z} \\ v_pmatrix}} \\\uff06= {{pmatrix} cos alpha sin cos cos cos cos cosma -aLpha alpha \uff06-COS ALPHA COS BETA COS BETA COS BETA COS BETA COS BETA COS BETA COS BETA COS BETA COS GAMMA BETA END {PMATRIX}} {begin {pmatrix} v_ {x} \\ v_ {y} \\ v_ {z} End {eND}} {z}\u3002 \u5927\u4f1a [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b9f\u969b\u306eeulerwinkel\u306e\u8ef8\u3092\u9078\u629e\u3059\u308b\u306b\u306f\u30016\u3064\u306e\u7570\u306a\u308b\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u8ab0\u306b\u3068\u3063\u3066\u3082\u3001\u6700\u521d\u30683\u756a\u76ee\u306e\u8ef8\u306f\u540c\u3058\u3067\u3059\u3002 6\u3064\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u4e21\u65b9 \u30ab\u30eb\u30c0\u30f3\u306e\u89d2\u5ea6 \uff08Gerolamo cardano\u306b\u3088\u308b\u3068\uff09\u307e\u305f\u306f \u30c6\u30a4\u30c8\u30fb\u30d6\u30e9\u30a4\u30a2\u30f3\u306e\u89d2\u5ea6 \uff08\u30d4\u30fc\u30bf\u30fc\u30fb\u30ac\u30b9\u30ea\u30fc\u30fb\u30c6\u30a4\u30c8\u3068\u30b8\u30e7\u30fc\u30b8\u30fb\u30cf\u30fc\u30c8\u30ea\u30fc\u30fb\u30d6\u30e9\u30a4\u30a2\u30f3\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\uff093\u3064\u306e\u56de\u8ee2\u306f\u30013\u3064\u306e\u7570\u306a\u308b\u8ef8\u306e\u5468\u308a\u306b\u884c\u308f\u308c\u307e\u3059\u3002\u5b9f\u969b\u306e\u30d5\u30af\u30ed\u30a6\u306e\u89d2\u5ea6\u3068\u540c\u69d8\u306b\u30016\u3064\u306e\u53ef\u80fd\u306a\u306d\u3058\u308c\u304c\u3042\u308a\u307e\u3059\u3002 \u30ed\u30fc\u30eb\u3001\u30cb\u30c3\u30af\u3001\u8caa\u6b32\u306a\u89d2\u5ea6\uff1az-ys-x\u2033\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8aac\u660e [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  Z\u3001Y ‘\u3001X’ ‘\uff08Greed-nick\u30ed\u30fc\u30eb\uff09\u306e\u30bb\u30c3\u30c8\u30cb\u30f3\u30b0 \u9752 \uff1araumfestes\u5ea7\u6a19\u7cfb \u7dd1 \uff1ay’-axis = node line n\uff08y ‘\uff09 \u8150\u6557 \uff1a\u30dc\u30c7\u30a3\u8010\u6027\u5ea7\u6a19\u7cfb \u6ce8\u91c8\uff1a th {displaystyletheta} \u3053\u3053\u3067\u306f\u30cd\u30ac\u30c6\u30a3\u30d6\u3067\u3059\u3002  \u8caa\u6b32\u3001\u30cb\u30c3\u30af\u3001\u30ed\u30fc\u30e9\u30fc\u306e\u89d2\u5ea6 \uff08 \u03c6 \u3001 th \u3001 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle\uff08psi\u3001theta\u3001varphi\uff09} \u822a\u7a7a\u6a5f\u306e\u89d2\u5ea6\u3068\u3057\u3066 \u822a\u7a7a\u3001\u51fa\u8377\u3001\u81ea\u52d5\u8eca\u5efa\u8a2d\u306e\u4f7f\u7528\u304a\u3088\u3073\u6a19\u6e96\u5316\uff08\u822a\u7a7a\uff1aDIN 9300; Automobilbau\uff1aDIN ISO 8855\uff09\u8ca9\u58f2\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u3001Tait Bryan\u30bf\u30fc\u30f3\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3057\u3066\u3044\u307e\u3059\u3002\u57fa\u6e96\u3067\u306f\u3001\u540d\u524d\u306f\u8caa\u6b32\u3001\u30cb\u30c3\u30af\u3001\u30ed\u30fc\u30eb\u30a2\u30f3\u30b0\u30eb\uff08\u82f1\u8a9e\u3067\u3059\u3002 \u30e8\u30fc \u3001 \u30d4\u30c3\u30c1 \u3068 \u30ed\u30fc\u30eb\u30a2\u30f3\u30b0\u30eb \uff093\u3064\u306e\u30aa\u30a4\u30e9\u30fc\u30a6\u30a3\u30f3\u30b1\u30eb\u306b\u51e6\u65b9\u3055\u308c\u307e\u3057\u305f\u3002 3\u3064\u306e\u56de\u8ee2\u306b\u3088\u308a\u3001\u5730\u7403\u796d\u306f \u30d0\u30c4 \u3068 \u3068 {displaystyle xyz}  – \u30b7\u30b9\u30c6\u30e0\uff08Engl\u3002 \u30ef\u30fc\u30eb\u30c9\u30d5\u30ec\u30fc\u30e0 \uff09\u30dc\u30c7\u30a3\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb \u30d0\u30c4 \u3068 \u3068 {displaystyle xyz} -Coodinate\u7cfb\uff08\u82f1\u8a9e \u30dc\u30c7\u30a3\u30d5\u30ec\u30fc\u30e0 \uff09\u5411\u304d\u3092\u5909\u3048\u305f\u3002 \u672c\u8cea\u7684\u306a\u9806\u5e8f \u3068 {displaystyle with}  –  \u3068 ‘ {displaystyle y ‘}  –  \u30d0\u30c4 \u300c {displaystyle x ”} \uff08gier-nick roll-anger\uff09\uff1a \u5916\u56e0\u6027\u3053\u308c\u306f\u9806\u5e8f\u306b\u5bfe\u5fdc\u3057\u307e\u3059 \u30d0\u30c4 {displaystyle x}  –  \u3068 {displaystyle y}  –  \u3068 {displaystyle with} \uff08Roll-nick-Greed\u89d2\u5ea6\uff09\u3002 \u5c0f\u3055\u306a\u6587\u5b57\u306e\u4ee3\u308f\u308a\u306b \u03c6 {displaystyle psi} \u3001 th {displaystyletheta} \u3068 \u30d5\u30a1\u30a4 {displaystyle varphi} \u5bfe\u5fdc\u3059\u308b\u5927\u6587\u5b57\u3082\u3042\u308a\u307e\u3059 \u03c6 {displaystyle psi} \u3001 th {displaystyletheta} \u3068 \u30d5\u30a1\u30a4 {displaystylephi} \u4f7f\u7528\u6e08\u307f\u3002 TransformationSmatrizen [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30dc\u30c7\u30a3\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\u304b\u3089\u7a7a\u9593\u8010\u6027\u5ea7\u6a19\u7cfb\u3078\u306e\u5ea7\u6a19\u5909\u63db\u306f\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4ecb\u3057\u3066\u884c\u308f\u308c\u307e\u3059 RGNR=Rz(\u03c8)Ry(\u03b8)Rx(\u03c6)=(cos\u2061\u03c8\u2212sin\u2061\u03c80sin\u2061\u03c8cos\u2061\u03c80001)(cos\u2061\u03b80sin\u2061\u03b8010\u2212sin\u2061\u03b80cos\u2061\u03b8)(1000cos\u2061\u03c6\u2212sin\u2061\u03c60sin\u2061\u03c6cos\u2061\u03c6)=(cos\u2061\u03b8cos\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8\u2212cos\u2061\u03c6sin\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8+sin\u2061\u03c6sin\u2061\u03c8cos\u2061\u03b8sin\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8+cos\u2061\u03c6cos\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03c6cos\u2061\u03c8\u2212sin\u2061\u03b8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6cos\u2061\u03b8)} 1nd {pmatrix}}} {begin {pmatrix} cos theta\uff060\uff06sin theta \\ 0\uff061\uff060 \\ -sin theta\uff060\uff060\uff06cos theta end arphi end {pmatrix}} \\\uff06= {begin {pmatrix}\u30b7\u30a7\u30bf\u30fb\u30b3\u30b9\u30fb\u30d7\u30b7 +sin varphi sin psi \\ cos sin sin psi\uff06sin a sin psi +cos varphi cos psi\uff06cos varphi sin theta sin psi -sin varphi cos psi \\ -sin theta\uff06sin varphi cos cos cos varphi cos cos enda end \u8aac\u660e\u3055\u308c\u305f\u3002\u5b87\u5b99\u30d5\u30a7\u30b9\u30c6\u30a3\u30d0\u30eb\u304b\u3089\u30dc\u30c7\u30a3\u30d7\u30eb\u30fc\u30d5\u5ea7\u6a19\u7cfb\u3078\u306e\u9006\u5909\u63db\u306f\u3001\u3053\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u8ee2\u7f6e\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8aac\u660e\u3055\u308c\u307e\u3059\u3002 \uff08\u5b9f\u969b\u306b\u306f\u9006\u3067\u3059\u304c\u3001\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u5834\u5408\u3001\u9006\u306f\u8ee2\u7f6e\u3055\u308c\u305f\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\uff09 RGNRT=Rx(\u03c6)TRy(\u03b8)TRz(\u03c8)T=(1000cos\u2061\u03c6sin\u2061\u03c60\u2212sin\u2061\u03c6cos\u2061\u03c6)(cos\u2061\u03b80\u2212sin\u2061\u03b8010sin\u2061\u03b80cos\u2061\u03b8)(cos\u2061\u03c8sin\u2061\u03c80\u2212sin\u2061\u03c8cos\u2061\u03c80001)=(cos\u2061\u03b8cos\u2061\u03c8cos\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03b8sin\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8\u2212cos\u2061\u03c6sin\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8+cos\u2061\u03c6cos\u2061\u03c8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8+sin\u2061\u03c6sin\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03c6cos\u2061\u03c8cos\u2061\u03c6cos\u2061\u03b8)} \\ 0 & cos Varphi & Sin Varphi \\ 0 & -sin Varphi & COS VARPHI END PSI & SIN PSI & 0 \\ -SIN PSI & COS PSI & 0 \\ 0 & 0 & 1nd {pmatrix}} \\ & = {Begin {PMATRIX} PHI SIN THETA SIN PSI +COS VARPHI COS PSI & SIN VARPHI COS THETA \\ aligned}}} \u3064\u307e\u308a\u3001\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059 v\u2192{displaystyle {thing {v}}} \u7a7a\u9593\u8010\u6027\u30b7\u30b9\u30c6\u30e0\u306e\u5ea7\u6a19 \u306e \u30d0\u30c4 {displaystyle v_ {x}} \u3001 \u306e \u3068 {displaystyle v_ {y}} \u3001 \u306e \u3068 {displaystyle v_ {z}} \u305d\u3057\u3066\u3001\u8eab\u4f53\u8010\u6027\u30b7\u30b9\u30c6\u30e0\u306e\u5ea7\u6a19 \u306e \u30d0\u30c4 {displaystyle v_ {x}} \u3001 \u306e \u3068 {displaystyle v_ {y}} \u3001 \u306e \u3068 {displaystyle v_ {z}} \u9069\u7528\u3055\u308c\u307e\u3059 (vxvyvz)=(cos\u2061\u03c8\u2212sin\u2061\u03c80sin\u2061\u03c8cos\u2061\u03c80001)(cos\u2061\u03b80sin\u2061\u03b8010\u2212sin\u2061\u03b80cos\u2061\u03b8)(1000cos\u2061\u03c6\u2212sin\u2061\u03c60sin\u2061\u03c6cos\u2061\u03c6)(vXvYvZ)=(cos\u2061\u03b8cos\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8\u2212cos\u2061\u03c6sin\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8+sin\u2061\u03c6sin\u2061\u03c8cos\u2061\u03b8sin\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8+cos\u2061\u03c6cos\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03c6cos\u2061\u03c8\u2212sin\u2061\u03b8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6cos\u2061\u03b8)(vXvYvZ)} end {pmatrix}}} {begin {pmatrix} cos theta\uff060\uff06sin theta \\ 0\uff061\uff060 \\ -sin theta\uff060\uff06cos theta end phi end {pmatrix}}} {begin {pmatrix} v_ {x} \\ v_ {y \\ v_} {x} \\ v_ {z} \\ v_ {x \\ v_} {begin {pmatrix} os varphi sin theta cos psi + sin varphi sin psi \\ cos theta sin psi\uff06sin varphi sin sin psi + os theta end {pmatrix}} {begin {pmatrix} v_ {x} \\ v_ {pmad} {pmad} {z} {z} {z} {z} {z} {z} {z} {z} {z} {z} {pmad}\uff09 }} \u3068 (vXvYvZ)=(1000cos\u2061\u03c6sin\u2061\u03c60\u2212sin\u2061\u03c6cos\u2061\u03c6)(cos\u2061\u03b80\u2212sin\u2061\u03b8010sin\u2061\u03b80cos\u2061\u03b8)(cos\u2061\u03c8sin\u2061\u03c80\u2212sin\u2061\u03c8cos\u2061\u03c80001)(vxvyvz)=(cos\u2061\u03b8cos\u2061\u03c8cos\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03b8sin\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8\u2212cos\u2061\u03c6sin\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8+cos\u2061\u03c6cos\u2061\u03c8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8+sin\u2061\u03c6sin\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03c6cos\u2061\u03c8cos\u2061\u03c6cos\u2061\u03b8)(vxvyvz)} varphi end {pmatrix}}} {begin {pmatrix} cos theta\uff060\uff06-sin theta \\ 0\uff061\uff060 \\ sin theta\uff060\uff060\uff060\uff060\uff060\uff060\uff060\uff06cos theta end {pmatrix}} {begin {pmatrix} 0\uff061nd {pmatrix} {pmaTrix} {pmaTrix} {pmaTrix} {pmaTrix} {pmaTrix} } \\ v_ {z} end {pmatrix}} \\\uff06= {begin {pmatrix} os psi -cos varphi sin psi\uff06sin varphi sin theta sin psi +cos cos psi\uff06sin varphi cos theta \\ os theta end {pmatrix} {pm} {pm} {pm} {firix}} v_ {z} end {pmatrix}} end {aligned}}}}} \u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u4f8b [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u91cd\u91cf\u30d9\u30af\u30c8\u30eb G\u2192{displaystyle {vec {g}}} \u5730\u7403\u796d\u306b\u53c2\u52a0\u3057\u3066\u3044\u307e\u3059 \u30d0\u30c4 \u3068 \u3068 {displaystyle xyz} -Coodinate\u7cfb\u306f1\u3064\u3060\u3051\u3067\u3059 \u3068 {displaystyle with} -komponente\uff08\u5730\u7403\u306e\u4e2d\u5fc3\u306b\u5411\u304b\u3063\u3066\uff09\uff1a G\u2192E= (00mg){displaystyle {vec {g}} _ {e} = {begin {pmatrix} 0 \\ 0 \\ mgend {pmatrix}}}} \u822a\u7a7a\u6a5f\u3078\u306e\u5909\u63db\u306f\u3001\u5730\u7403\u8010\u6027\u30d9\u30af\u30bf\u30fc\u306e\u4e57\u7b97\u306b\u3088\u3063\u3066\u767a\u751f\u3057\u307e\u3059 G\u2192\u3068 {displaystyle {vec {g}} _ {e}} \u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u4ed8\u304d r g n r t {displaystyle r_ {gnr}^{t}} \uff1a G\u2192F=RGNRTG\u2192E=(cos\u2061\u03b8cos\u2061\u03c8cos\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03b8sin\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8\u2212cos\u2061\u03c6sin\u2061\u03c8sin\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8+cos\u2061\u03c6cos\u2061\u03c8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6sin\u2061\u03b8cos\u2061\u03c8+sin\u2061\u03c6sin\u2061\u03c8cos\u2061\u03c6sin\u2061\u03b8sin\u2061\u03c8\u2212sin\u2061\u03c6cos\u2061\u03c8cos\u2061\u03c6cos\u2061\u03b8)(00mg)=(\u2026\u2026\u2212sin\u2061\u03b8\u2026\u2026sin\u2061\u03c6cos\u2061\u03b8\u2026\u2026cos\u2061\u03c6cos\u2061\u03b8)(00mg)=(\u2212sin\u2061\u03b8sin\u2061\u03c6cos\u2061\u03b8cos\u2061\u03c6cos\u2061\u03b8)mg} \\ sin varphi sin theta cos psi -cos varphi sin psi\uff06sin varphi sin sin psi +cos varphi cos psi\uff06sin varphi cos cos theta \\ cos varphi sin theta cos psi\uff06cos varphi cos cos theta end {pmatrix}} {begin\uff06cos varphi varphi end {pmaTrix} }} \u4f53\u91cd\u306f\u7269\u7406\u7684\u306b\u6b63\u3057\u3044\u3067\u3059 G\u2192{displaystyle {vec {g}}} \u65e2\u5b58\u306e\u30cb\u30c3\u30af\u30a6\u30a3\u30f3\u30b1\u30eb\u3067 th {displaystyletheta} \u305f\u3068\u3048\u3070\u3001\u98db\u884c\u6a5f\u3067\u3082\u5f8c\u65b9\u306b\uff08\u8ca0\u306e \u30d0\u30c4 {displaystyle x} -\u65b9\u5411\uff09\u3002 \u56de\u8ee2\u8ef8\u306e\u9806\u5e8f\u3092\u9078\u629e\u3059\u308b\u305f\u3081\u306b\u3001\u7d50\u679c\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u6b21\u306e\u63a5\u7d9a\uff08\u30a2\u30af\u30c6\u30a3\u30d6\u30bf\u30fc\u30f3\uff09\u306e\u52a9\u3051\u306b\u3088\u3063\u3066\u7c21\u5358\u306b\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002 [7] \u30b0\u30ed\u30fc\u30d0\u30eb\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u65e2\u77e5\u3067\u3059\u3002\u3053\u308c\u304c\u3059\u3067\u306b\u306d\u3058\u308c\u305f\u8ef8\u306e\u5468\u308a\u306b\u518d\u3073\u56de\u3055\u308c\u308b\u5834\u5408\u3001\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u5bfe\u5fdc\u3059\u308b\u30b0\u30ed\u30fc\u30d0\u30eb\u8ef8\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u304c\u3001\u5909\u63db\u3055\u308c\u305f\u30d9\u30af\u30c8\u30eb\u30d9\u30fc\u30b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u5909\u63db\u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff08\u57fa\u672c\u5909\u5316\u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff09\u306f\u3001\u307e\u3055\u306b\u4ee5\u524d\u306e\u56de\u8ee2\u3067\u3059\u3002 \u306a\u308c a {displaystyle a} \u3068 b {displaystyle b} 2\u3064\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u8ef8\u306e\u5468\u308a\u306e2\u3064\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9 g {displaystyle g} \u3068 h {displaystyle h} \u3002\u30ed\u30fc\u30bf\u30ea\u30fc\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u9806\u5e8f\u306b\u8a08\u7b97\u3057\u307e\u3059 \uff08 g \u3001 h ‘ \uff09\uff09 {displaystyle\uff08g\u3001h^{prime}\uff09} \u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u304c2\u56de\u76ee\u306e\u56de\u8ee2\u306e\u305f\u3081\u306b\u3042\u308b\u3053\u3068\u3092\u89b3\u5bdf\u3057\u305f\u5834\u5408 h {displaystyle h} \u57fa\u672c\u30de\u30c8\u30ea\u30c3\u30af\u30b9 B~= a b a  –  \u521d\u3081 {displaystyle {tilde {b}} = aba^{-1}} \u5bfe\u5fdc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7d50\u679c\u306e\u7dcf\u5c04\u6483\u884c\u5217\u304c\u5f97\u3089\u308c\u307e\u3059 c = B~a = a b a  –  \u521d\u3081 a = a b {displaystyle c = {tilde {b}} a = aba^{ –  1} a = ab} \u3002\u3088\u308a\u591a\u304f\u306e\u56de\u8ee2\u306e\u5834\u5408\u3001\u8a3c\u660e\u306f\u540c\u69d8\u3067\u3059\u3002 3\u3064\u306e\u30a2\u30af\u30c6\u30a3\u30d6\u30bf\u30fc\u30f3\uff08A\u304c\u6700\u521d\u306b\u5b9f\u884c\u3055\u308c\u3001\u6b21\u306bB\u3001\u6b21\u306bc\uff09\u3067\u7dcf\u5c04\u6483\u884c\u5217\u304c\u7d50\u679c\u3092\u3082\u305f\u3089\u3057\u307e\u3059 d = \uff08 \uff08 a b \uff09\uff09 de c de \uff08 a b \uff09\uff09 t \uff09\uff09 de \uff08 a de b de a t \uff09\uff09 de a = a b c {displaystyle d =\uff08\uff08ab\uff09cdot ccdot {\uff08ab\uff09}^{t}\uff09cdot\uff08acdot bcdot a^{t}\uff09cdot a = abc} \u306e\u4f7f\u7528\u4e2d a t = a  –  \u521d\u3081 {displaystyle a^{t} = a^{-1}} \u3001 \uff08 a de b \uff09\uff09 t = b t de a t {displaystyle {\uff08acdot b\uff09}^{t} = b^{t} cdot a^{t}} \u3002 \u3053\u306e\u8868\u73fe\u306f\u3001\u9023\u7d9a\u3057\u305f\u8ef8\u306e\u56de\u8ee2\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u9006\u306e\u9806\u5e8f\u3067\u306f\u3042\u308b\u304c\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u5ea7\u6a19\u8ef8\u306e\u5468\u308a\u306e\u56de\u8ee2\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u5358\u7d14\u306a\u4e57\u7b97\u306b\u8d77\u56e0\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002 \u8ef8\u3092\u4f7f\u7528\u3057\u305f\u5f97\u3089\u308c\u305f\u5ea7\u6a19\u7cfb \u30d0\u30c4 \u300c {displaystyle x ”} \u3001 \u3068 \u300c {displaystyle y ”} \u3068 \u3068 \u300c {disspastyle with ”} SO -CALLED BODY -PROOF\u30b7\u30b9\u30c6\u30e0\u3067\u3059\u3002\u89d2\u5ea6 \u03d5 {displaystylephi} \u3068 th {displaystyletheta} \u306e\u5834\u6240\u3092\u4e0e\u3048\u307e\u3059 \u3068 \u300c {disspastyle with ”}  – \u8010\u6027\u30b7\u30b9\u30c6\u30e0\uff08\u300c\u56de\u8ee2\u300d\u304a\u3088\u3073\u300c\u50be\u659c\u300d\uff09\u3068\u6bd4\u8f03\u3057\u305f\u30de\u30c3\u30b1\u30b9;\u89d2\u5ea6 \u03c6 {displaystyle psi} \u3042\u306a\u305f\u306e\u5468\u308a\u306e\u4f53\u306e\u9053\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u540d\u524d\u306e\u898f\u5247\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002 \u95a2\u9023\u3059\u308b\u30ed\u30fc\u30bf\u30ea\u30fc\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u30aa\u30a4\u30e9\u30fc\u89d2\u306b\u5272\u308a\u5f53\u3066\u308b\u30a4\u30e9\u30b9\u30c8\u306b\u306f\u3001\u3053\u306e\u5272\u308a\u5f53\u3066\u304c\u5c40\u6240\u7684\u306b\u53ef\u9006\u7684\u3067\u306f\u306a\u304f\u3001\u30b8\u30f3\u30d0\u30eb\u30ed\u30c3\u30af\u306b\u3064\u3044\u3066\u8a71\u3059\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u304c\u3042\u308a\u307e\u3059\u3002\u4e0a\u968e\u306e\u5834\u5408\u3002 x\u307e\u305f\u306fy\u306e\u898f\u5247\u306f\u30012\u756a\u76ee\u306e\u56de\u8ee2\u89d2\u304c\u30bc\u30ed\u306b\u306a\u308a\u3001\u6700\u521d\u306e\u56de\u8ee2\u306e\u56de\u8ee2\u30d9\u30af\u30c8\u30eb\u304c2\u756a\u76ee\u306e\u56de\u8ee2\u306e\u56de\u8ee2\u30d9\u30af\u30c8\u30eb\u3068\u540c\u3058\u3067\u3042\u308b\u5834\u5408\u306b\u5e38\u306b\u767a\u751f\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u305d\u308c\u306f\u305d\u308c\u304c\u5468\u308a\u306e\u56de\u8ee2\u306e\u305f\u3081\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059 \u3068 {displaystyle with} -Ouler-Winkel\u3068\u540c\u3058\u3088\u3046\u306b a = \u3068 + \u3068 ‘ {\u5c55\u793aalpha = z+z ‘} \u4e0e\u3048\u307e\u3059\u3002 \u822a\u7a7a\u57fa\u6e96\u306e\u5f8c\u306b\u4f4d\u7f6e\u89d2\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u304d\u3001\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059 th = \u00b1 \u03c02{displaystyle Text Style theta = PM {frac {pi} {2}}} \u3002 \u30ab\u30fc\u30c8\u30fb\u30de\u30b0\u30ca\u30b9\u306e\u5f8c [8] \u30b8\u30e3\u30a4\u30ed\u306e\u554f\u984c\u304c\u3042\u308a\u307e\u3059 th = 0 {displaystyletheta = 0} \u30d5\u30af\u30ed\u30a6\u306e\u89d2\u5ea6\uff08X\u30b3\u30f3\u30d9\u30f3\u30b7\u30e7\u30f3\uff09\u3092\u4f7f\u7528\u3057\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u4ee3\u308f\u308a\u306bCardWort\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 Euler-Winkel\u306b\u306f\u3001\u56de\u8ee2\u3092\u8868\u3059\u305f\u3081\u306e\u3044\u304f\u3064\u304b\u306e\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\u3002 \u4e0a\u8a18\u306e\u7279\u7570\u70b9\u306f\u3001\u7570\u306a\u308b\u30aa\u30a4\u30e9\u30fc\u30bf\u30fc\u30f3\u306b\u3088\u3063\u3066\u5358\u4e00\u306e\u56de\u8ee2\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30b8\u30f3\u30d0\u30eb\u30ed\u30c3\u30af\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u73fe\u8c61\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 \u30aa\u30a4\u30e9\u30fc\u30b7\u30b9\u30c6\u30e0\u3067\u306e\u56de\u8ee2\u306e\u6b63\u3057\u3044\u7d44\u307f\u5408\u308f\u305b\u306f\u3001\u56de\u8ee2\u306e\u8ef8\u304c\u5909\u5316\u3059\u308b\u305f\u3081\u3001\u76f4\u611f\u7684\u306b\u6307\u5b9a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002 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\u7406\u8ad6\u7269\u7406\u5b66\u3067\u306f\u3001\u30aa\u30a4\u30e9\u30fc\u306e\u89d2\u5ea6\u3092\u4f7f\u7528\u3057\u3066\u525b\u4f53\u3092\u8a18\u8ff0\u3057\u307e\u3059\u3002\u5b9f\u7528\u7684\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u30ab\u30eb\u30c0\u30f3\u30b5\u30b9\u30da\u30f3\u30b7\u30e7\u30f3\u3092\u3082\u305f\u3089\u3057\u307e\u3059 [11] \u6280\u8853\u7684\u306a\u30e1\u30ab\u30cb\u30ba\u30e0\u3002 \u8eca\u4e21\u306e\u5834\u5408\u3001\u4e3b\u8981\u306a\u72b6\u6cc1\u306e\u30aa\u30a4\u30e9\u30fc\u30a6\u30a3\u30f3\u30b1\u30eb\u306f\u3001\u30ed\u30fc\u30eb\u30cb\u30c3\u30af\u30b0\u30ea\u30fc\u30c9\u89d2\u3068\u547c\u3070\u308c\u307e\u3059\u3002 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\u3002 \uff08 \u9650\u3089\u308c\u305f\u30d7\u30ec\u30d3\u30e5\u30fc Google Book\u691c\u7d22\u3067\uff09\u3002  \u300c3\u3064\u306e\u9023\u7d9a\u3057\u305f\u30bf\u30fc\u30f3\u3092\u4f7f\u7528\u3057\u3066\u3001\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u7cfb\u304b\u3089\u5225\u306e\u7cfb\u3078\u306e\u5909\u63db\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7279\u5b9a\u306e\u9806\u5e8f\u3067\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u300d  \u2191  Hui Cheng\u3001K\u3002C\u3002Gupta\uff1a \u6700\u7d42\u56de\u8ee2\u306b\u95a2\u3059\u308b\u6b74\u53f2\u7684\u306a\u30e1\u30e2 \u3002\u306e\uff1a Journal of Applied Mechanics \u3002 \u30d0\u30f3\u30c9  56 \u3001 \u3044\u3044\u3048\u3002  \u521d\u3081 \u30011989\u5e743\u6708\u3001 S.  139\u2013145 \u3001doi\uff1a 10.1115\/1,3176034 \uff08 \u5168\u6587 [PDF; 2018\u5e7412\u670813\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  L. eulerus\uff1a \u3059\u3079\u3066\u306e\u525b\u4f53\u306e\u7ffb\u8a33\u306e\u305f\u3081\u306e\u4e00\u822c\u7684\u306a\u5f0f \u3002\u306e\uff1a \u65b0\u3057\u3044\u89e3\u8aac\u79d1\u5b66\u30a2\u30ab\u30c7\u30df\u30fc\u30da\u30c8\u30ed\u30dd\u30ea\u30bf\u30ca\u30a8 \u3002 \u30d0\u30f3\u30c9  20\uff081775\uff09 \u30011776\u3001 S.  189\u2013207 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 \u82f1\u8a9e\u7ffb\u8a33[PDF; 188  KB ; 2018\u5e7412\u670813\u65e5\u306b\u30a2\u30af\u30bb\u30b9] \u79fb\u884c \u3053\u3053\u3067\u306e\u52d5\u304d\u306f\u3042\u308a\u307e\u3059\uff09\u3002   \u2191  L. eulerus\uff1a \u6c7a\u5b9a\u3059\u308b\u65b0\u3057\u3044\u52d5\u6a5f\u306e\u65b9\u6cd5 \u3002\u306e\uff1a \u65b0\u3057\u3044\u89e3\u8aac\u79d1\u5b66\u30a2\u30ab\u30c7\u30df\u30fc\u30da\u30c8\u30ed\u30dd\u30ea\u30bf\u30ca\u30a8 \u3002 \u30d0\u30f3\u30c9  20\uff081775\uff09 \u30011776\u3001 S.  208\u2013238 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [PDF; 1.6  MB ; 2018\u5e7412\u670813\u65e5\u306b\u53d6\u5f97]\u65b9\u7a0b\u5f0f\u306f\u00a713\u306b\u3042\u308a\u307e\u3059\uff09\u3002   \u2191 a b c  Leonardus eulerus\uff1a \u56fa\u5b9a\u3055\u308c\u305f\u643a\u5e2f\u96fb\u8a71\u306e\u5468\u308a\u306e\u4f53\u306e\u52d5\u304d \u3002\u306e\uff1a \u30ec\u30ca\u30fc\u30c9\u30aa\u30a4\u30e9\u30fc\u30aa\u30da\u30e9POTEMA\u6570\u5b66\u3068\u7269\u7406\u5b66\uff1a1844\u5e74\u306b\u958b\u793a \u3002 \u30d0\u30f3\u30c9  2 \u30011862\u5e74\u3001 S.  43\u201362 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [PDF; 1.4  MB ; 2018\u5e7412\u670813\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   –  \u95a2\u9023\u3059\u308b\u30a4\u30e9\u30b9\u30c8  \u2191 a b c  \u7d0d\u5c4b\uff1a \u5206\u6790\u529b\u5b66 \u3002 G\u00f6ttingen1797\uff08 \u30b9\u30ad\u30e3\u30f3 [PDF; 2018\u5e7412\u670813\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\u30aa\u30ea\u30b8\u30ca\u30eb\u30bf\u30a4\u30c8\u30eb\uff1a \u5206\u6790\u529b\u5b66 \u3002 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Euler-Wiege\u3001Geosciences\u306e\u8f9e\u66f8\u3001Spectrum       (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\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22892#breadcrumbitem","name":"Eulersche Winkel -Wikipedia"}}]}]