[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/107585#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/107585","headline":"\u6e26\u5ea6 – Wikipedia","name":"\u6e26\u5ea6 – Wikipedia","description":"\u5317\u534a\u7403\u306b\u304a\u3051\u308b\u9ad8\u6c17\u5727 (H) \u30fb\u4f4e\u6c17\u5727 (L) \u306e\u56de\u8ee2\u65b9\u5411 \u6e26\u5ea6\uff08\u3046\u305a\u3069\u3001\u304b\u3069\uff09\u306f\u3001\u6d41\u308c\u306e\u56de\u8ee2\u3059\u308b\u3042\u308a\u3055\u307e\u3092\u8868\u73fe\u3059\u308b\u91cf\u3067\u3042\u308b\u3002\u6e26\u5ea6\u306f\u30d9\u30af\u30c8\u30eb\u91cf\uff08\u3055\u3089\u306b\u8a00\u3048\u3070\u64ec\u30d9\u30af\u30c8\u30eb\uff09\u3067\u3042\u308a\u3001\u6d41\u308c\u306e\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u30d9\u30af\u30c8\u30eb\u5834\u306e\u56de\u8ee2\u3067\u3042\u308b\u3002 \u6e26\u5ea6\u30d9\u30af\u30c8\u30eb \u03a9 \u306f\u6d41\u901f\u30d9\u30af\u30c8\u30eb v = (vx, vy, vz) \u306b\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3002 \u03a9=rot\u2061v=\u2207\u00d7v=(\u2202vz\u2202y\u2212\u2202vy\u2202z,\u2202vx\u2202z\u2212\u2202vz\u2202x,\u2202vy\u2202x\u2212\u2202vx\u2202y){displaystyle {begin{aligned}{boldsymbol {Omega }}&=operatorname {rot}","datePublished":"2022-03-23","dateModified":"2022-03-23","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/9\/98\/BuysBallot_en.svg\/200px-BuysBallot_en.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/9\/98\/BuysBallot_en.svg\/200px-BuysBallot_en.svg.png","height":"107","width":"200"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/107585","about":["Wiki"],"wordCount":3845,"articleBody":"  \u5317\u534a\u7403\u306b\u304a\u3051\u308b\u9ad8\u6c17\u5727 (H) \u30fb\u4f4e\u6c17\u5727 (L) \u306e\u56de\u8ee2\u65b9\u5411\u6e26\u5ea6\uff08\u3046\u305a\u3069\u3001\u304b\u3069\uff09\u306f\u3001\u6d41\u308c\u306e\u56de\u8ee2\u3059\u308b\u3042\u308a\u3055\u307e\u3092\u8868\u73fe\u3059\u308b\u91cf\u3067\u3042\u308b\u3002\u6e26\u5ea6\u306f\u30d9\u30af\u30c8\u30eb\u91cf\uff08\u3055\u3089\u306b\u8a00\u3048\u3070\u64ec\u30d9\u30af\u30c8\u30eb\uff09\u3067\u3042\u308a\u3001\u6d41\u308c\u306e\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u30d9\u30af\u30c8\u30eb\u5834\u306e\u56de\u8ee2\u3067\u3042\u308b\u3002\u6e26\u5ea6\u30d9\u30af\u30c8\u30eb \u03a9 \u306f\u6d41\u901f\u30d9\u30af\u30c8\u30eb v = (vx, vy, vz) \u306b\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3002\u03a9=rot\u2061v=\u2207\u00d7v=(\u2202vz\u2202y\u2212\u2202vy\u2202z,\u2202vx\u2202z\u2212\u2202vz\u2202x,\u2202vy\u2202x\u2212\u2202vx\u2202y){displaystyle {begin{aligned}{boldsymbol {Omega }}&=operatorname {rot} {boldsymbol {v}}=nabla times {boldsymbol {v}}\\&={begin{pmatrix}{dfrac {partial v_{z}}{partial y}}-{dfrac {partial v_{y}}{partial z}},&{dfrac {partial v_{x}}{partial z}}-{dfrac {partial v_{z}}{partial x}},&{dfrac {partial v_{y}}{partial x}}-{dfrac {partial v_{x}}{partial y}}end{pmatrix}}end{aligned}}}\u6e26\u5ea6\u30d9\u30af\u30c8\u30eb\u3092\u6d41\u7dda\u306e\u3088\u3046\u306b\u3064\u306a\u3052\u305f\u66f2\u7dda\u3092\u6e26\u7dda\u3068\u3044\u3046\u3002\u6d41\u308c\u306e\u4e2d\u306e\u3042\u308b\u9589\u66f2\u7dda\u4e0a\u306e\u5404\u70b9\u3092\u901a\u308b\u6e26\u7dda\u306b\u3088\u3063\u3066\u3067\u304d\u308b\u66f2\u9762\u3092\u6e26\u7ba1\u3068\u3044\u3046\u3002\u65ad\u9762\u7a4d\u3092\u7121\u9650\u5c0f\u306b\u3057\u305f\u6e26\u7ba1\u3092\u6e26\u7cf8\u3068\u3044\u3046[\u6ce8 1]\u3002\u6e26\u7cf8\u304c\u9589\u66f2\u7dda\u306b\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u308c\u3092\u6e26\u8f2a\u3068\u3044\u3046[1][2]\u3002\u6d41\u308c\u306e\u4e2d\u306b\u5fae\u5c0f\u9818\u57df\u3092\u3068\u3063\u305f\u3068\u304d\u3001\u5fae\u5c0f\u6642\u9593\u3067\u8003\u3048\u308c\u3070\u3001\u305d\u306e\u9818\u57df\u306f\u6e26\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u3092\u8ef8\u306b\u89d2\u901f\u5ea6 (1\/2)|\u03c9| \u3067\u525b\u4f53\u7684\u306b\u56de\u8ee2\u3059\u308b\u30021\u672c\u306e\u6e26\u7ba1\u3092\u8003\u3048\u305f\u3068\u304d\u3001\u6e26\u7ba1\u306e\u8868\u9762\u3092\u4e00\u5468\u3059\u308b\u4efb\u610f\u306e\u9589\u66f2\u7dda \u2202S \u306b\u6cbf\u3063\u305f\u5faa\u74b0\uff08\u6e26\u5ea6 \u03c9 \u306e\u9762\u7a4d\u5206\uff09\u0393=\u222e\u2202Sv\u22c5ds=\u222bS\u03c9\u22c5dS{displaystyle Gamma =oint _{partial S}{boldsymbol {v}}cdot mathrm {d} {boldsymbol {s}}=int _{S}{boldsymbol {omega }}cdot mathrm {d} {boldsymbol {S}}}\u306f\u3001\u6e26\u7ba1\u306b\u56fa\u6709\u306e\u91cf\u3068\u306a\u308a\u3001\u6e26\u7ba1\u306e\u5f37\u3055\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u3053\u3067 ds \u306f\u9589\u66f2\u7dda \u2202S \u306e\u7dda\u8981\u7d20\u3001dS \u306f \u2202S \u3067\u56f2\u307e\u308c\u308b\u66f2\u9762\u306e\u9762\u8981\u7d20\u3067\u3042\u308b\u3002\u540c\u69d8\u306b\u3001\u6e26\u7cf8\u306b\u5bfe\u3057\u3066\u305d\u306e\u65ad\u9762\u7a4d \u03c3 \u3068\u6e26\u5ea6 \u03c9 \u3068\u306e\u7a4d \u0393 = \u03c3\u03c9 \u306f\u6e26\u7cf8\u306b\u56fa\u6709\u306e\u91cf\u3067\u3042\u308a\u3001\u6e26\u7cf8\u306e\u5f37\u3055\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u3001\u6e26\u7cf8\u304c\u7d30\u3044\u3068\u3053\u308d\u307b\u3069\u6e26\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u6e26\u7ba1\u3084\u6e26\u7cf8\u306f\u6d41\u4f53\u5185\u90e8\u306e\u70b9\u3067\u9014\u5207\u308c\u308b\u3053\u3068\u306f\u306a\u304f\u3001\u6d41\u4f53\u9818\u57df\u306e\u5883\u754c\uff08\u7121\u9650\u9060\u3092\u542b\u3080\uff09\u307e\u3067\u4f38\u3073\u3066\u3044\u308b\u304b\u3001\u9589\u66f2\u7dda\u3068\u306a\u308a\u6e26\u8f2a\u3092\u4f5c\u308b\u304b\u306e\u3069\u3061\u3089\u304b\u3067\u3042\u308b\u3002Table of Contents\u30c6\u30f3\u30bd\u30eb\u3068\u3057\u3066\u306e\u6027\u8cea[\u7de8\u96c6]\u30d3\u30aa\u30fb\u30b5\u30d0\u30fc\u30eb\u306e\u6cd5\u5247[\u7de8\u96c6]\u6e26\u5ea6\u65b9\u7a0b\u5f0f[\u7de8\u96c6]\u5927\u6c17\u529b\u5b66\u306b\u304a\u3051\u308b\u6e26\u5ea6[\u7de8\u96c6]\u6ce8\u91c8[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u30c6\u30f3\u30bd\u30eb\u3068\u3057\u3066\u306e\u6027\u8cea[\u7de8\u96c6]\u6e26\u5ea6\u306f\u3001\u901f\u5ea6\u52fe\u914d\u30c6\u30f3\u30bd\u30eb\u306e\u53cd\u5bfe\u79f0\u6210\u5206(\u2202[ivj])=12(0\u2202v1\u2202x2\u2212\u2202v2\u2202x1\u2202v1\u2202x3\u2212\u2202v3\u2202x1\u2202v2\u2202x1\u2212\u2202v1\u2202x20\u2202v2\u2202x3\u2212\u2202v3\u2202x2\u2202v3\u2202x1\u2212\u2202v1\u2202x3\u2202v3\u2202x2\u2212\u2202v2\u2202x30){displaystyle {big (}partial _{[i}v_{j]}{big )}={frac {1}{2}}{begin{pmatrix}0&{dfrac {partial v_{1}}{partial x_{2}}}-{dfrac {partial v_{2}}{partial x_{1}}}&{dfrac {partial v_{1}}{partial x_{3}}}-{dfrac {partial v_{3}}{partial x_{1}}}\\\\{dfrac {partial v_{2}}{partial x_{1}}}-{dfrac {partial v_{1}}{partial x_{2}}}&0&{dfrac {partial v_{2}}{partial x_{3}}}-{dfrac {partial v_{3}}{partial x_{2}}}\\\\{dfrac {partial v_{3}}{partial x_{1}}}-{dfrac {partial v_{1}}{partial x_{3}}}&{dfrac {partial v_{3}}{partial x_{2}}}-{dfrac {partial v_{2}}{partial x_{3}}}&0end{pmatrix}}}  \u3092\u3001\u95a2\u4fc2\u5f0f12(\u2202vi\u2202xj\u2212\u2202vj\u2202xi)=\u03f5jik\u03c9k{displaystyle {frac {1}{2}}left({frac {partial v_{i}}{partial x_{j}}}-{frac {partial v_{j}}{partial x_{i}}}right)=epsilon _{jik}omega _{k}}\u3092\u7528\u3044\u3066\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u8868\u3057\u305f\u3082\u306e\u3067\u3042\u308b[3]\u3002\u3053\u3053\u3067 \u03b5 \u306f\u30a8\u30c7\u30a3\u30f3\u30c8\u30f3\u306e\u30a4\u30d7\u30b7\u30ed\u30f3\u3067\u3042\u308b\u3002  \u30d3\u30aa\u30fb\u30b5\u30d0\u30fc\u30eb\u306e\u6cd5\u5247[\u7de8\u96c6]\u7121\u9650\u306b\u5e83\u304c\u308b\u6d41\u4f53\u9818\u57df\u306e\u6e26\u5ea6\u5206\u5e03\u304c\u4e0e\u3048\u3089\u308c\u3066\u304a\u308a\u3001\u304b\u3064\u7121\u9650\u9060\u3067\u901f\u5ea6\u304c0\u3067\u3042\u308b\u3068\u304d\u3001\u901f\u5ea6\u5206\u5e03\u306f\u30d3\u30aa\u30fb\u30b5\u30d0\u30fc\u30eb\u306e\u6cd5\u5247\u306b\u3088\u308a\u6c42\u3081\u3089\u308c\u308b\u3002v=14\u03c0\u222d\u03c9\u00d7rr2dV=rot\u2061\u222d\u03c94\u03c0rdV{displaystyle {begin{aligned}{boldsymbol {v}}&={frac {1}{4pi }}iiint {frac {{boldsymbol {omega }}times {boldsymbol {r}}}{r^{2}}}dV\\&=operatorname {rot} iiint {frac {boldsymbol {omega }}{4pi r}}dVend{aligned}}}\u6e26\u5ea6\u65b9\u7a0b\u5f0f[\u7de8\u96c6]\u6d41\u4f53\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u56de\u8ee2\u3092\u53d6\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u6b21\u306e\u6e26\u5ea6\u65b9\u7a0b\u5f0f\u304c\u5c0e\u304b\u308c\u308b\u3002  \u2202\u03c9\u2202t=rot\u2061(v\u00d7\u03c9)+\u03bd\u22072\u03c9{displaystyle {frac {partial {boldsymbol {omega }}}{partial t}}=operatorname {rot} ({boldsymbol {v}}times {boldsymbol {omega }})+nu nabla ^{2}{boldsymbol {omega }}}\u3053\u3053\u3067\u03bd\u306f\u6d41\u4f53\u306e\u52d5\u7c98\u6027\u4fc2\u6570\u3067\u3042\u308b\u3002\u5927\u6c17\u529b\u5b66\u306b\u304a\u3051\u308b\u6e26\u5ea6[\u7de8\u96c6]\u5927\u6c17\u529b\u5b66\u306b\u304a\u3044\u3066\u306f\u3001\u6e26\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u4e2d\u30673\u65b9\u5411\u306e\u6210\u5206\u306e\u4e2d\u3067\u7279\u306b\u91cd\u8981\u306a\u306e\u306f\u925b\u76f4\u65b9\u5411\u306e\u6210\u5206\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u925b\u76f4\u6e26\u5ea6\u3068\u547c\u3070\u308c\u3001\u5358\u306b\u6e26\u5ea6\u3068\u3044\u3063\u305f\u5834\u5408\u3001\u6697\u9ed9\u306e\u4e86\u89e3\u3068\u3057\u3066\u925b\u76f4\u6e26\u5ea6\u3092\u6307\u3059\u3053\u3068\u304c\u591a\u3044\u3002\u925b\u76f4\u6e26\u5ea6\u306f\u3001\u6771\u897f\u5357\u5317\u65b9\u5411\u306e\u9577\u65b9\u5f62\u306e\u5358\u4f4d\u9818\u57df\u306b\u5bfe\u3057\u3066\u3001\u9577\u65b9\u5f62\u306e\u8fba\u306b\u6cbf\u3046\u65b9\u5411\u306e\u98a8\u901f\u3092\u8003\u3048\u3001\uff08\u4e0a\u8fba\u306e\u897f\u5411\u304d\u306e\u98a8\u901f\uff0d\u4e0b\u8fba\u306e\u897f\u5411\u304d\u306e\u98a8\u901f\uff09\uff0f\u7e26\u65b9\u5411\u306e\u8ddd\u96e2  – 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