[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/8259#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/8259","headline":"\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53 – Wikipedia","name":"\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53 – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09 \u591a\u69d8\u4f53 M \u304c\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53\uff08\u30dd\u30a2\u30bd\u30f3\u305f\u3088\u3046\u305f\u3044\u3001\u82f1: Poisson Manifold\uff09\u3067\u3042\u308b\u3068\u306f\u3001M \u4e0a\u306e C\u221e \u7d1a\u95a2\u6570\u5168\u4f53\u306e\u306a\u3059\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092 C\u221e(M) \u3068\u8868\u3059\u3068\u304d\u3001\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u5199\u50cf {\u22c5,\u22c5}:C\u221e(M)\u00d7C\u221e(M)\u2192C\u221e(M){displaystyle","datePublished":"2021-07-25","dateModified":"2021-07-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/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\/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\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/8259","about":["Wiki"],"wordCount":2941,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09\u591a\u69d8\u4f53 M \u304c\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53\uff08\u30dd\u30a2\u30bd\u30f3\u305f\u3088\u3046\u305f\u3044\u3001\u82f1: Poisson Manifold\uff09\u3067\u3042\u308b\u3068\u306f\u3001M \u4e0a\u306e C\u221e \u7d1a\u95a2\u6570\u5168\u4f53\u306e\u306a\u3059\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092 C\u221e(M) \u3068\u8868\u3059\u3068\u304d\u3001\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u5199\u50cf {\u22c5,\u22c5}:C\u221e(M)\u00d7C\u221e(M)\u2192C\u221e(M){displaystyle {cdot ,cdot }colon C^{infty }(M)times C^{infty }(M)to C^{infty }(M)}   \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u3044\u3046\u3002{\u22c5,\u22c5}{displaystyle {cdot ,cdot }} \u306f\u3001R{displaystyle mathbb {R} }-\u53cc\u7dda\u5f62\u5f62\u5f0f\u3067\u3042\u308b\u3002{f,g}=\u2212{g,f}{displaystyle ,{f,g}=-{g,f},}{{f,g},h}+{{g,h},f}+{{h,f},g}=0{displaystyle ,{{f,g},h}+{{g,h},f}+{{h,f},g}=0,}\u3000:\u30e4\u30b3\u30d3\u5f8b{f,gh}=g{f,h}+h{f,g}{displaystyle ,{f,gh}=g{f,h}+h{f,g},}\u3053\u306e\u3068\u304d\u3001\u5199\u50cf {\u22c5,\u22c5}:C\u221e(M)\u00d7C\u221e(M)\u2192C\u221e(M){displaystyle {cdot ,cdot }colon C^{infty }(M)times C^{infty }(M)to C^{infty }(M)} \u3092 M \u4e0a\u306e\u30dd\u30a2\u30bd\u30f3\u69cb\u9020\u3001\u3082\u3057\u304f\u306f\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27\u3068\u547c\u3076\u3002  (M,\u03c9){displaystyle ,(M,omega ),} \u3092\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u591a\u69d8\u4f53\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001M{displaystyle M}\u4e0a\u306b\u30dd\u30a2\u30bd\u30f3\u69cb\u9020\u304c\u6b21\u306e\u3088\u3046\u306b\u3057\u3066\u5b9a\u7fa9\u3067\u304d\u308b\u3002  {f,g}=\u03c9(Xf,Xg){displaystyle ,{f,g}=omega (X_{f},X_{g}),}\u3053\u3053\u3067\u3001Xf,Xg{displaystyle ,X_{f},X_{g},} \u306f\u305d\u308c\u305e\u308c f,g{displaystyle ,f,g,} \u304b\u3089\u5b9a\u307e\u308b\u30cf\u30df\u30eb\u30c8\u30f3\u30d9\u30af\u30c8\u30eb\u5834\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u591a\u69d8\u4f53\u306f\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53\u3067\u3082\u3042\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53\u304c\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u591a\u69d8\u4f53\u3067\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3002(q1,\u22ef,qn,p1,\u22ef,pn){displaystyle (q_{1},cdots ,q_{n},p_{1},cdots ,p_{n})} \u3092\u30c0\u30eb\u30d6\u30fc\u5ea7\u6a19\u3068\u3059\u308b\u3068\u3001\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u591a\u69d8\u4f53\u4e0a\u306e\u30dd\u30a2\u30bd\u30f3\u69cb\u9020\u306f\u3001{f,g}=\u2211i=1n(\u2202f\u2202pi\u2202g\u2202qi\u2212\u2202f\u2202qi\u2202g\u2202pi){displaystyle {f,g}=sum _{i=1}^{n}left({frac {partial f}{partial p_{i}}}{frac {partial g}{partial q_{i}}}-{frac {partial f}{partial q_{i}}}{frac {partial g}{partial p_{i}}}right)}\u3068\u66f8\u3051\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/8259#breadcrumbitem","name":"\u30dd\u30a2\u30bd\u30f3\u591a\u69d8\u4f53 – Wikipedia"}}]}]