{"id":8305,"date":"2021-12-20T02:21:24","date_gmt":"2021-12-19T18:21:24","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=8305"},"modified":"2021-12-20T02:21:24","modified_gmt":"2021-12-19T18:21:24","slug":"%e6%88%91%e7%9a%84%e5%93%81%e5%91%b3","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8305","title":{"rendered":"\u6211\u7684\u201c\u54c1\u5473\u201d"},"content":{"rendered":"
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\u5728\u957f\u671f\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u6211\u5bf9\u4e00\u4ef6\u4e8b\u7684\u786e\u8ba4\u4e0d\u65ad\u5730\u5f3a\u5316\uff0c\u90a3\u5c31\u662f\u6211\u8ddfClifford Truesdell\u548cWalter Noll\u6709\u7740\u76f8\u540c\u7684\u201c\u54c1\u5473\u201d\u3002<\/p>\n\n\n\n

\u6211\u8d5e\u540c\u5e76\u6b23\u8d4f\u5df2\u6709\u7269\u7406\u7406\u8bba\u7684\u516c\u7406\u5316\u52aa\u529b\u3002\u6211\u8ba4\u4e3a\u8fd9\u662f\u4e00\u4e2a\u6709\u610f\u4e49\u7684\u7814\u7a76\u9886\u57df\u3002\u6211\u5e0c\u671b\u6709\u4e00\u5929\u6211\u4eec\u7684\u672c\u79d1\u6559\u6750\u80fd\u66ff\u6362\u6210\u8fd9\u4e00\u9886\u57df\u7684\u7814\u7a76\u6210\u679c\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u5728\u6d41\u53d8\u5b66\u8bb2\u4e49\u4e2d\u5c31\u5c1d\u8bd5\u9075\u5faa\u4e00\u4e9b\u5df2\u7ecf\u5efa\u7acb\u7684\u516c\u7406\u5316\u5f15\u5165\u3002<\/p>\n\n\n\n

\u6211\u7b2c\u4e00\u6b21\u770b\u5230Water Noll\u7684neo-classical space-time\u6784\u5efa\u662f\u5728\u4e0b\u9762\u8fd9\u4e2a\u5730\u65b9\uff1a<\/p>\n\n\n\n

W. Noll (1966), The Foundations of Mechanics, In: G. Grioli, C. Truesdell (eds), Non-linear Continuum Theories, Springer-Verlag<\/p>\n\n\n\n

\u8fd9\u4e66\u7684\u5370\u5237\u662f\u7528\u6253\u5b57\u673a\u7684\uff0c\u6709\u5f88\u82b1\u4f53notation\u662f\u540e\u9762\u518d\u7528\u624b\u5199\u8865\u4e0a\u7684\u3002\u6211\u4e0d\u77e5\u9053\u8fd9\u4e9b\u7b14\u8ff9\u662f\u4e0d\u662fNoll\u672c\u4eba\u7684\u3002\u4f46\u4ece\u6392\u7248\u4e0a\u53ef\u4ee5\u8bf4\u662f\u975e\u5e38\u4e0d\u53cb\u597d\u3002\u6211\u5bf9\u65f6\u7a7a\u6784\u5efa\u7684\u5185\u5bb9\u4e5f\u5b8c\u5168\u964c\u751f\u3002\u4f46\u662f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48\uff0c\u6211\u4e00\u5f00\u59cb\u5c31\u611f\u53d7\u5230\u8fd9\u4e2a\u8bdd\u9898\u662f\u5f88\u53ef\u80fd\u611f\u5174\u8da3\u7684\uff0c\u9b3c\u4f7f\u795e\u5dee\u5730\u628a\u5b83\u786c\u5543\u5b8c\u4e86\uff0c\u679c\u7136\u611f\u53d7\u5230\u4e86\u65e0\u6cd5\u7528\u8a00\u8bed\u5f62\u5bb9\u7684\u7f8e\u5b66\u4eab\u53d7\u3002\u9664\u4e86\u7f8e\u7684\u4eab\u53d7\u4e4b\u5916\uff0c\u65f6\u7a7a\u6784\u5efa\u7684\u4e25\u5bc6\u6027\uff0c\u53ef\u4ee5\u8ba9\u540e\u7eed\u7684\u5f88\u591a\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u5f53\u4e0b\u6559\u6750\u4e2d\u5bb9\u6613\u8ba9\u5b66\u751f\u641e\u6df7\u7684\u8bdd\u9898\u53d8\u5f97\u6839\u672c\u4e0d\u53ef\u80fd\u641e\u6df7\u3002<\/p>\n\n\n\n

\u65e9\u671f\uff0c\u6211\u8865\u4e60\u6570\u5b66\u7684\u552f\u4e00\u53c2\u8003\u5c31\u662f<\/p>\n\n\n\n

S. Hassani (1999), Mathematical Physics: A Modern Introduction to Its Foundations, Springer<\/p>\n\n\n\n

\u6211\u77e5\u9053\u8fd9\u672c\u4e66\uff0c\u4e5f\u662f\u4ece\u65e9\u5e74\u6d41\u4f20\u7684\u201cFang\u7684\u4e66\u5355\u201d\u4e2d\u77e5\u9053\u7684\u3002\u8fd9\u672c\u4e66\u5bf9Fang\u800c\u8a00\u662f\u65b0\u4e66\uff0c\u4ed6\u53ea\u662f\u8bf4\u597d\u50cf\u8fd8\u53ef\u4ee5\u3002\u73b0\u5728\u56de\u770b\uff0c\u8fd9\u672c\u4e66\u7ed9\u4e86\u6211\u4e24\u4e2a\u5f71\u54cd\uff1a1\uff09\u662f\u8fd9\u672c\u4e66\u5185\u5bb9\u5f88\u5168\uff0c\u4e14\u5728\u4e00\u672c\u4e66\u4e4b\u5185Notation\u548c\u6982\u5ff5\u4f53\u7cfb\u662f\u7edf\u4e00\u7684\u3002\u8ba9\u6211\u5728\u521a\u5b66\u6570\u5b66\u5c31\u611f\u53d7\u5230\u4e86\u4e16\u4e0a\u53ea\u6709\u4e00\u4e2a\u6570\u5b66\uff0c\u800c\u4e0d\u662f\u5272\u88c2\u770b\u4f3c\u65e0\u5173\u7684\u4e0d\u540c\u8bfe\u7a0b\u3002\u540e\u8005\u53ef\u80fd\u662f\u5f88\u591a\u6570\u5b66\u6216\u7269\u7406\u4e13\u4e1a\u7684\u672c\u79d1\u751f\u5728\u73b0\u5728\u7684\u6559\u80b2\u4f53\u7cfb\u4e2d\u83b7\u5f97\u7684\u5370\u8c61\u30022\uff09\u7531\u4e8e\u8981\u505a\u52301\uff09\u8fd9\u4e66\u4e0d\u53ef\u907f\u514d\u5730\u8981\u5982\u5176\u526f\u6807\u9898\u6240\u8a00\u6bd4\u8f83\u73b0\u4ee3\u3002\u4f8b\u5982\u6240\u6709\u6784\u5efa\u90fd\u4ece\u96c6\u5408\u51fa\u53d1\uff0ccoordinate-free\u7684\u7ebf\u6027\u4ee3\u6570\uff0c\u628a\u5f20\u91cf\u5f15\u5165\u4e3a\u591a\u7ebf\u6027\u5f62\u5f0f\u7b49\u3002\u4e4b\u524d\u4e00\u5ea6\u6709\u4e00\u70b9\u8ba9\u6211\u5f88\u8be7\u5f02\u7684\u662f\uff0c\u4e3a\u4ec0\u4e48\u6211\u770b\u8fc7\u4e00\u4e9b\u4e66\uff0c\u5728\u77e5\u4e4e\u4e0a\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u611f\u89c9\u5c31\u662f\u6211\u770b\u5f97\u61c2\u90a3\u4e9b\u79d1\u73ed\u51fa\u8eab\u7684\u4eba\u8bf4\u4ec0\u4e48\uff0c\u8fd8\u597d\u50cf\u80fd\u5bf9\u4e00\u4e9b\u8d85\u8d8a\u672c\u79d1\u7684\u8bdd\u9898\u8fdb\u884c\u8bc4\u8bba\u3002\u5982\u679c\u4e0d\u5b8c\u5168\u662f\u9519\u89c9\uff0c\u90a3\u53ef\u80fd\u662f\u56e0\u4e3a\u6211\u4e00\u5f00\u59cb\u5c31\u63a5\u89e6\u73b0\u4ee3\u7684\u6570\u5b66\u6587\u672c\u3002<\/p>\n\n\n\n

\u540e\u6765\u6211\u4eceHassani\u7684\u4e66\u540e\u53c2\u8003\u4e66\u76ee\u53c8\u76f4\u63a5\u6216\u95f4\u63a5\u5730\u77e5\u9053\u4e86\u5f88\u591a\u4e66\u548c\u4f5c\u8005\u3002\u4f8b\u5982Halmos\u548c Hoffman and Kunze\u7684\u7ebf\u6027\u4ee3\u6570\u3002\u540e\u8005\u6210\u4e3a\u4e86\u6211\u7b2c\u4e00\u672c\u4e3b\u8981\u5b66\u4e60\u7684\u4e66\u3002Hoffman and Kunze\u5176\u5b9e\u662f\u4e00\u672c\u5904\u5904\u900f\u7740\u62bd\u8c61\u4ee3\u6570\u7684\u666e\u901a\u7ebf\u6027\u4ee3\u6570\uff0ccoordinate-free\u7684\u8272\u5f69\u66f4\u6d53\u4e86\u3002\u4e00\u4e2a\u8ba9\u6211\u66fe\u7ecf\u56f0\u60d1\uff0c\u5374\u53cd\u800c\u662f\u6781\u5176\u5177\u6709\u542f\u53d1\u6027\u7684\u7279\u70b9\u662f\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u7ebf\u6027\u4ee3\u6570\uff0c\u5168\u4e66\u6ca1\u6709\u201ccross product\u201d\u8fd9\u4e2a\u8bcd\u3002\u7ffb\u904d\u5168\u4e66\u53ea\u6709tensor product\u6ca1\u6709tensor\uff0c\u8fdb\u884ctensor product\u7684\u5bf9\u8c61\u53eb\u591a\u7ebf\u6027\u5f62\u5f0f\u3002\u73b0\u5728\u56de\u60f3\u8d77\u6765\uff0c\u6211\u6562\u8bf4\u5f88\u591a\u529b\u5b66\u8bfe\u7a0b\u7684\u8bb2\u8ff0\u8005\u4e0e\u8bb8\u672a\u5fc5\u80fd\u89e3\u7b54\u5b66\u751f\u5728\u4e00\u5207\u5176\u4ed6\u4e0d\u540c\u5730\u65b9\u770b\u5230\u7528\u201c\u5f20\u91cf\u201d\u4e8c\u5b57\u79f0\u547c\u7684\u5bf9\u8c61\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u4e1c\u897f\uff0c\u6709\u4ec0\u4e48\u8054\u7cfb\u3002<\/p>\n\n\n\n

\u8d2f\u7a7f\u6211\u6559\u5b66\u7684\u4e00\u79cd\u503e\u5411\u5c31\u662f\u5e0c\u671b\u4f20\u8fbe\u77e5\u8bc6\u7684\u7edf\u4e00\u6027\uff0c\u4e00\u79cd\u5173\u4e8e\u4e16\u754c\u7684\u4e00\u5143\u8bba\u3002\u6211\u5f88\u538c\u70e6\u7684\u4e00\u79cd\u770b\u6cd5\u5c31\u662f\uff0c\u5728\u8fd9\u4e2a\u8bfe\u4f60\u5c31\u8fd9\u6837\u6765\uff0c\u5230\u4e86\u90a3\u4e2a\u8bfe\u4e86\u4f60\u53c8\u5c31\u90a3\u6837\u6765\u3002\u524d\u9762\u5b66\u8fc7\u7684\u77e5\u8bc6\uff0c\u597d\u50cf\u6709\u4e9b\u9053\u7406\uff0c\u4f46\u5728\u540e\u9762\u7684\u8bfe\u603b\u662f\u65e0\u6cd5\u76f4\u63a5\u4f7f\u7528\u3002\u4e00\u4e2a\u4eba\u5728\u5b66\u751f\u65f6\u671f\u8981\u540c\u65f6\u638c\u63e1\u5f88\u591a\u5272\u88c2\u7684\u8bfe\u7a0b\u77e5\u8bc6\uff0c\u800c\u5b83\u4eec\u7684\u878d\u6c47\u8d2f\u901a\u5219\u8981\u9760\u6bcf\u4e00\u4e2a\u4eba\u5728\u65e5\u540e\u804c\u4e1a\u751f\u6daf\u4e2d\u7684\u4e2a\u4eba\u7684\u3001\u79c1\u4e0b\u7684\u3001\u4e5f\u8bb8\u5f88\u6c11\u79d1\u7684\u603b\u7ed3\uff0c\u6216\u8005\u66f4\u591a\u60c5\u51b5\u4e0b\u5e72\u8106\u662f\u5fd8\u5374\u6216\u653e\u5f03\u3002<\/p>\n\n\n\n

coordinate-free\u5176\u5b9e\u662f\u7ebf\u6027\u4ee3\u6570\u7684\u5176\u4e2d\u4e00\u79cd\u54c1\u5473\u3002\u73b0\u5728\u5728\u77e5\u4e4e\u4e0a\u6d41\u884c\u7740\u4e00\u79cd\u6279\u8bc4\u4ee5\u77e9\u9635\u4ee3\u6570\u4e3a\u4e3b\u7684\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u3002\u7531\u4e8e\u8fd9\u662f\u56fd\u5185\u6559\u6750\u6d41\u884c\u7684\u4f53\u4f8b\uff0c\u8fd9\u79cd\u6279\u8bc4\u53c8\u9644\u5e26\u7740\u5305\u62ec\u5bf9\u56fd\u5185\u6559\u5b66\u843d\u540e\u7684\u6279\u8bc4\u3002\u4f46\u4e8b\u5b9e\u4e0a\u7ebf\u6027\u4ee3\u6570\u6559\u6750\u4e00\u76f4\u6709\u4e24\u79cd\u4f20\u7edf\u3002\u77e9\u9635\u4ee3\u6570\u8fd9\u79cd\u662f\u5341\u4e5d\u4e16\u7eaa\u672b\u4e8c\u5341\u4e16\u7eaa\u521d\u552f\u4e00\u7684\u4e3b\u6d41\u3002coordinate-free\u662f\u6bd4\u8f83\u73b0\u4ee3\u7684\u98ce\u683c\uff0c\u662f\u968f\u7740\u62bd\u8c61\u4ee3\u6570\u7684\u53d1\u5c55\u4e4b\u540e\u53cd\u4f5c\u7528\u4e8e\u672c\u79d1\u7ebf\u6027\u4ee3\u6570\u6559\u5b66\u4e0a\u7684\u7ed3\u679c\u3002\u800c\u5c31\u7b97\u540e\u8005\u66f4\u73b0\u4ee3\uff0c\u5728\u540e\u8005\u51fa\u73b0\u540e\u4e5f\u8fd8\u6709\u4eba\u559c\u6b22\u6309\u524d\u8005\u7684\u65b9\u5f0f\u5199\u4e66\uff0c\u6d41\u884c\u5168\u7403\uff0c\u90a3\u4f8b\u5982\u90a3\u672c\u201cLinear Algebra Done Right\u201d\uff0c\u8fd8\u6709C. Lay\u7684\u90a3\u672c\u3002<\/p>\n\n\n\n

\u5f53\u7136\uff0c\u6211\u672c\u4eba\u559c\u6b22\u62bd\u8c61\u4ee3\u6570\u7684\u54c1\u5473\u3002\u5177\u4f53\u8bf4\u7684\u8bdd\uff0c\u8fd9\u53ef\u80fd\u6765\u81eaBourbaki\u3002\u4f46\u6211\u6700\u521d\u4e5f\u662f\u6709\u6559\u5b66\u4e0a\u7684\u5b9e\u9645\u52a8\u673a\u7684\u3002\u6211\u5e0c\u671b\u6211\u7684\u6d41\u53d8\u5b66\u8bfe\u7a0b\u662f\u4ecb\u7ecd\u57fa\u4e8e\u5f20\u91cf\u7684\u672c\u6784\u5173\u7cfb\u7684\uff0c\u8fd9\u91cc\u9762\u4e00\u4e2a\u6700\u91cd\u8981\u7684\u601d\u60f3\u5c31\u662f\u6807\u67b6\u4e0d\u53d8\u6027\u3002\u6574\u4e2a33\u8bfe\u65f6\u7684\u6d41\u53d8\u5b66\u8bfe\uff0c\u8ddf\u9ad8\u5206\u5b50\u6750\u6599\u6027\u8d28\u76f8\u5173\u7684\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u672c\u6784\u7684\u7f57\u5217\uff0c\u6211\u53ea\u82b1\u4e86\u4e00\u4e24\u8bfe\u65f6\uff0c\u5269\u4e0b\u768432\u8bfe\u65f6\u4e00\u534a\u662f\u5728\u6253\u6570\u5b66\u57fa\u7840\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u8fde\u7eed\u4ecb\u529b\u5b66\u57fa\u7840\u3002\u56e0\u6b64\u6211\u4e00\u5b9a\u8981\u4ecb\u7ecd\u4e00\u5957\u65b9\u4fbf\u63cf\u8ff0\u548c\u7406\u89e3\u6807\u67b6\u4e0d\u53d8\u6027\u7684\u6570\u5b66\u8bed\u8a00\u3002\u4e00\u4e2a\u57fa\u4e8e\u77e9\u9635\u548c\u5750\u6807\u7684\u6570\u5b66\u57fa\u7840\u5fc5\u7136\u662f\u4e0d\u5229\u4e8e\u8fd9\u4e2a\u6559\u5b66\u76ee\u6807\u7684\u3002\u56e0\u6b64\u6211\u7684\u8bb2\u4e49\u5f88\u5c11\u51fa\u73b0\u5750\u6807\u548c\u77e9\u9635\u6765\u5b9a\u4e49\u6216\u5f15\u5165\u4ee3\u6570\u6982\u5ff5\uff0c\u603b\u662f\u903c\u8feb\u8bfb\u8005\u57fa\u4e8e\u96c6\u5408\u4e0e\u4ee3\u6570\u64cd\u4f5c\u6765\u7406\u89e3\u62bd\u8c61\u7684\u4ee3\u6570\u5bf9\u8c61\u3002\u800c\u4e14\u5728\u8bb2\u5fae\u79ef\u5206\u90e8\u5206\u7684\u65f6\u5019\uff0c\u4e5f\u5ef6\u7528\u4e86\u8fd9\u79cd\u98ce\u683c\uff0c\u867d\u7136\u5fae\u79ef\u5206\u548c\u6570\u5b66\u5206\u6790\u90e8\u5206\u6211\u662f\u53c2\u8003\u770b\u53e6\u5916\u7684\u4e66\u7684\uff08\u5fae\u79ef\u5206\u770bWCT 1965\uff0c\u6570\u5206\u770bRudin\uff09\uff0c\u4f46\u662f\u6211\u82b1\u5f88\u591a\u65f6\u95f4\u5c1d\u8bd5\u628a\u6570\u5b66\u5b9e\u8d28\u91cd\u65b0\u7528\u4ee3\u6570\u7684\u65b9\u5f0f\u63cf\u8ff0\u4e86\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u5728\u5f15\u5165Noll\u7684neo-Classical space-time\u4e4b\u524d\u6211\u8fd8\u4ecb\u7ecd\u4e86\u6b27\u51e0\u91cc\u5f97\u51e0\u4f55\u7684\u4e00\u4e2a\u6bd4\u8f83\u73b0\u4ee3\u7684\u6784\u5efa\uff0c\u540c\u6837\u4ec5\u4f7f\u7528\u7528\u8bb2\u4e49\u5185\u7684\u6982\u5ff5\u548cnotation\u3002\u5173\u4e8e\u7269\u4f53\u53ca\u5176\u8d28\u91cf\u7684\u516c\u7406\u5316\u5f15\u5165\uff0c\u6211\u53c8\u6076\u8865\u4e86\u6d4b\u5ea6\u8bba\uff0c\u4f46\u8fd9\u4e2a\u77e5\u8bc6\u6211\u662f\u4f9d\u9760\u7f51\u4e0a\u7684\u8bb2\u4e49\u7684\u3002\u73b0\u5728\u8fd8\u6ca1\u5b8c\u5168\u5f04\u597d\u7684\u70b9\u662f\uff0c\u7531\u4e8e\u4e25\u683c\u6765\u8bf4\u7269\u4f53\u5b9e\u9645\u4e0a\u4e0d\u662f\u4e00\u4e2asigma\u4ee3\u6570\uff0c\u800c\u662f\u4e00\u4e2a\u5e03\u5c14\u4ee3\u6570\uff1b\u7269\u4f53\u7684\u8d28\u91cf\u662f\u5728\u5e03\u5c14\u4ee3\u6570\u4e0a\u7684\u6d4b\u5ea6\uff0c\u800c\u5e76\u4e0d\u662f\u4e00\u4e2a\u52d2\u8d1d\u683c\u79ef\u5206\u3002\u56e0\u6b64\u5728\u8fd9\u79cd\u65b0\u57fa\u7840\u4e0a\u662f\u5426\u4ecd\u6709\u7edd\u5bf9\u8fde\u7eed\u7684\u7c7b\u4f3c\u6982\u5ff5\u548c\u62c9\u5c3c\u5b9a\u7406\u7684\u7c7b\u4f3c\u5b9a\u7406\u8fd8\u4e0d\u53ef\u77e5\u3002Truesdell\u5728\u4ed6\u81ea\u5df1\u7684\u8457\u4f5c\u4e2d\u6ca1\u6709\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u7136\u540e\u8bf4\u8bfb\u8005\u8981\u662f\u76f4\u63a5\u5f53\u4f5csigma\u4ee3\u6570\u548c\u52d2\u8d1d\u683c\u79ef\u5206\u4e5f\u6ca1\u4ec0\u4e48\u95ee\u9898\u3002\u76ee\u524d\u6211\u8bb2\u4e49\u5c31\u662f\u6d3b\u5728\u8fd9\u4e2a\u6a21\u7cca\u7684\u57fa\u7840\u4e0a<\/p>\n\n\n\n

Walter Noll\u4e5f\u6709\u7c7b\u4f3c\u7684\u54c1\u5473\u3002\u4ed6\u5199\u8fc7\u4e00\u672c\u4e66\uff1a<\/p>\n\n\n\n

Walter Noll (1987), Finite-Dimensional Spaces: Algebra, Geometry and Analysis. Vol. 1, Springer-Verlag<\/p>\n\n\n\n

\u8fd9\u672c\u4e66\u662f\u4f5c\u8005\u8ba4\u4e3a\u81ea\u5df1\u4e00\u751f\u4e2d\u6700\u91cd\u8981\u7684\u8457\u4f5c\u3002\u4ed6\u63cf\u8ff0\u8bf4\u8fd9\u672c\u4e66\u7684approach\u662f\u201cuncompromisingly coordinate-free and R^n-free when dealing with concepts\u201d\u3002\u8003\u8651\u5230\u8fd9\u672c\u4e66\u526f\u6807\u9898\u5305\u62ec\u4e86\u51e0\u4f55\u548c\u5206\u6790\uff0c\u5b83\u6070\u597d\u5b8c\u6210\u4e86\u6211\u52aa\u529b\u60f3\u8981\u5728\u8bb2\u4e49\u4e2d\u505a\u5230\u7684\u4e8b\u3002\u4f5c\u8005\u5728\u81ea\u8ff0\u4e2d\u8fd8\u8bf4\uff1a<\/p>\n\n\n\n

I have been accused of being  too “Bourbakistic”. I plead guilty. I believe the work of Bourbaki was the most important contribution to mathematics in the 20’th century. Bourbaki was not a single individual but a group, some of whose members I met personally. Bourbaki was started, in 1935, by some young French mathematicians who disliked the way mathematics was taught in France at the time. To quote from the book Bourbaki, a Secret Society of Mathematicians, by Maurice Mashaal: “Gradually, the group’s extensive reflections and lively discussions led to a new vision of mathematics, a modern way of teaching and even doing it.”<\/p>

In 1973 my colleague and friend Juan Schaffer and I became involved in an undergraduste honors program at CMU entitled “Mathematical Studies”. We  disliked the way mathematics was taught at the time and proposed a new way to present mathematics as an integrated whole and to avoid its traditional division into separate and seemingly unrelated courses, My involvement in this program finally lead to this treatise. Therefore, it is the result of a task similar to that undertaken by Bourbaki, albeit on a limited scale.<\/p>Noll’s papers (cmu.edu)<\/a><\/cite><\/blockquote>\n\n\n\n

\u5728\u4e66\u4e2d\u4ed6\u53c8\u8bf4\uff1a<\/p>\n\n\n\n

About 25 years ago I started to write notes for a course for seniors and beginning graduate students at Carnegie Institute of Technology (renamed Carnegie-Mellon University in 1968). At first, the course was entitled “Tensor Analysis”. I soon realized that what usually passes for “Tensor Analysis” is really an undigested mishmash of linear and multilinear algebra, differential calculus in finite-dimensional spaces, manipulation of curvilinear coordinates, and differential geometry on manifolds, all treated with mindless formalisms and without real insight. As a result, I omitted the abstract differential geometry, which is too difficult to be treated properly at this level, and renamed the course “Multidimensional Algebra, Geometry, and Analysis”, and later “Finite-Dimensional Spaces”. The notes were rewritten several times. <\/p> Walter Noll (1987), Finite-Dimensional Spaces: Algebra, Geometry and Analysis. Vol. 1, Springer-Verlag <\/cite><\/blockquote>\n\n\n\n

\u8fd9\u7b80\u76f4\u5c31\u662f\u590d\u8ff0\u4e86\u6211\u81ea\u5df1\u5728\u5b66\u4e60\u6570\u5b66\u65f6\u7684\u611f\u89c9\u3002\u6211\u66fe\u7ecf\u627e\u8fc7\u5176\u4ed6\u6807\u9898\u6709tensor\u7684\u4e0d\u540c\u7684\u4e66\uff0c\u60f3\u8981\u628a\u6570\u5b66\u548c\u7269\u7406\u5b66\u4e2d\u6240\u6709\u7528tensor\u6765\u79f0\u547c\u7684\u4e1c\u897f\u90fd\u5f52\u7eb3\u4e00\u4e0b\uff0c\u63d0\u53d6\u4ed6\u4eec\u7684\u5171\u6027\uff0c\u7136\u540e\u4ee5\u6070\u5f53\u5730\u3001\u7b80\u6d01\u800c\u53c8\u6709\u9884\u89c1\u6027\u7684\u8bed\u8a00\u5728\u8bfe\u5802\u4e0a\u544a\u8bc9\u5b66\u751f\uff0c\u5230\u5e95\u4ec0\u4e48\u662f\u5f20\u91cf\uff0c\u4e14\u8bf4\u5b8c\u540e\u5b83\u65e2\u89e3\u91ca\u4e86\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e2d\u51fa\u73b0\u7684\u5f20\u91cf\uff0c\u53c8\u8981\u80fd\u89e3\u91ca\u6570\u5b66\u4e66\u3001\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7b49\u4e00\u5207\u5b66\u751f\u5c06\u6765\u53ef\u80fd\u78b0\u5230\u88ab\u79f0\u4e3a\u201c\u5f20\u91cf\u201d\u7684\u4e1c\u897f\u3002\u5728\u8fd9\u8fc7\u7a0b\u4e2d\u6211\u63a5\u89e6\u5230\u53eb\u201ctensor analysis\u201d\u7684\u4e66\u6216\u8bdd\u9898\uff0c\u90fd\u4e00\u5f8b\u628a\u5f20\u91cf\u660e\u786e\u5730\u6216\u6697\u4e2d\u5730\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u5e26\u6709\u82e5\u5e72\u4e2a\u4e0a\u6807\u548c\u4e0b\u6807\u7684\u6570\u3001\u4e0a\u4e0b\u6807\u7684\u5404\u7c7b\u64cd\u4f5c\uff0c\u4ee5\u53ca\u66f2\u7ebf\u5750\u6807\u53d8\u6362\u539f\u7406\uff08Christ-Awful symbol\uff09\u3002\u4e00\u5f00\u59cb\u6211\u89c9\u5f97\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u5b8c\u5168\u4e0d\u8003\u8651\u4e0e\u5176\u4ed6\u6570\u5b66\u8854\u63a5\u7684\u6570\u5b66\u4e66\uff08\u81f3\u5c11\uff0c\u5b83\u4e0d\u4ece\u96c6\u5408\u51fa\u53d1\u5b9a\u4e49\u4e49\u81ea\u5df1\u7684\u6982\u5ff5\uff09\u5f88\u4e0d\u201c\u4e13\u4e1a\u201d\u3002\u540e\u6765\u6211\u660e\u767d\u4e3a\u4ec0\u4e48\u4f1a\u5145\u65a5\u8fd9\u79cd\u4e66\u3002\u8fd9\u4e2a\u77e5\u8bc6\u662f\u4f9b\u8981\u5b66\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7684\u5b66\u751f\u6076\u8865\u6570\u5b66\u4e0e\u8a00\u7528\u7684\u3002\u6f5c\u53f0\u8bcd\u5c31\u662f\u8fd9\u4e00\u5957\u6570\u5b66\u64cd\u4f5c\u4f60\u53cd\u6b63\u8981\u7528\uff0c\u5b66\u61c2\u5b66\u5bf9\u5c31\u662f\u4e86\uff0c\u8003\u8bd5\u505a\u9898\u5c31\u80fd\u62ff\u5230\u5206\uff0c\u4e00\u79cd\u201c\u4f1a\u7b97\u5c31\u884c\u201d\u903b\u8f91\u4e0b\u7684\u6570\u5b66\u4e66\u3002\u4e5f\u5c31\u662f\u5728\u5f88\u591a\u7c7b\u4f3c\u8fd9\u79cd\u4f53\u9a8c\u4e4b\u540e\uff0c\u6211\u7adf\u7136\u660e\u767d\u4e86\u4e00\u4e2a\u672c\u6765\u5e94\u8be5\u662f\u7269\u7406\u5b66\u4e13\u4e1a\u7684\u4eba\u624d\u6709\u4f53\u9a8c\u7684\u73b0\u72b6\uff0c\u90a3\u5c31\u662f\u4ed6\u4eec\u7684\u6559\u5b66\u4f53\u7cfb\u5e76\u4e0d\u5c3d\u5982\u4eba\u610f\u3002Noll\u5728\u4e0a\u8ff0\u5f15\u6587\u4e2d\u5bf9\u5f53\u65f6\u6559\u5b66\u7684\u6279\u8bc4\uff0c\u73b0\u5728\u8fd8\u662f\u4e00\u6837\u3002<\/p>\n\n\n\n

Truesdell\u4e00\u5f00\u59cb\u5bf9\u5f20\u91cf\u7684\u7406\u89e3\u4e5f\u662f\u5750\u6807\u5f0f\u7684\u3002Walter Noll\u5728NFT\u7b2c3\u7248\u4e2d\u8bf4\uff0c\u4ed6\u5728\u535a\u58eb\u5b66\u4f4d\u8bba\u6587\u4e2d\u91c7\u7528\u4e00\u79cdcoordinate-free\u7684\u98ce\u683c\uff0cTruesdell\u4e0d\u4e60\u60ef\uff0c\u5f3a\u8febNoll\u8865\u4e0a\u5750\u6807\u53d8\u91cf\u8868\u8ff0\u3002\u4f46\u662f\u540e\u6765Truesdell\u63a5\u53d7\u4e86\u524d\u4e00\u79cd\u98ce\u683c\uff0c\u5728\u4e00\u5c01\u7ed9Noll\u7684\u4fe1\uff081958\uff09\u5199\u9053\uff1a<\/p>\n\n\n\n

“I must also admit that the direct notations you use are better suited to fundamental questions than are indicial notations. Your present mathematical style is smoother and simpler than that in your thesis.”<\/p>C. Truesdell, W. Noll (2004), The Non-Linear Field Theories of Mechanics, 3rd ed., Springer-Verlag<\/cite><\/blockquote>\n\n\n\n

\u6211\u4e5f\u5728\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\u5f88\u70e6summation rule\u3002\u51e1\u662f\u770b\u5230\u901a\u7bc7summation rule\u7684\u8bfe\u672c\u6211\u90fd\u5f03\u5982\u655d\u5c63\u3002\u6211\u8ba4\u4e3asummation rule\u5bf9\u4e8e\u7ecf\u5178\u529b\u5b66\u662f\u4e00\u4e2a\u5f88\u574f\u7684\u53d1\u660e\uff08\u4e5f\u8bb8\u5728\u5e7f\u4e49\u76f8\u5bf9\u8bba\u4e2d\u662f\u4e0d\u53ef\u66ff\u4ee3\u7684\uff0c\u4f46\u7ecf\u5178\u529b\u5b66\u7684\u7b80\u5355\u6027\u5b8c\u5168\u6ca1\u5fc5\u8981\uff09\uff1b\u5b83\u8ba9\u65b9\u7a0b\u7684\u7269\u7406\u601d\u60f3\u53d8\u5f97\u6a21\u7cca\u751a\u81f3\u6d88\u5931\u3002\u7269\u7406\u5b66\u5728\u7406\u8bba\u4e2d\u5bf9\u6570\u5b66\u7684\u4f7f\u7528\u7406\u5e94\u4f53\u73b0\u6570\u5b66\u601d\u60f3\u548c\u7269\u7406\u601d\u60f3\u7684\u7edf\u4e00\u6027\uff0c\u800c\u4e0d\u53ea\u662f\u628a\u6570\u5b66\u5f53\u4f5c\u8bed\u8a00\u548c\u5de5\u5177\u3002\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0asummation rule\u662f\u4e00\u79cd\u5197\u4f59\u4ea7\u7269\uff0c\u6216\u8005\u53c8\u662f\u201c\u4f1a\u7b97\u5c31\u884c\u201d\u601d\u60f3\u7684\u4ea7\u7269\u3002<\/p>\n\n\n\n

\u201c\u4f1a\u7b97\u5c31\u884c\u201d\uff0c\u662f\u5de5\u7a0b\u6559\u80b2\u7684\u4e00\u79cd\u98ce\u6c14\u3002\u201c\u65e0\u9700\u4f1a\u7b97\uff0c\u5374\u8981\u771f\u61c2\u201d\u7684\u601d\u60f3\u6216\u54c1\u5473\uff0c\u4e4b\u6240\u4ee5\u4f1a\u4ece\u6211\u8fd9\u513f\u4ea7\u751f\uff0c\u4e3b\u8981\u8fd8\u662f\u7531\u4e8e\u6211\u662f\u5316\u5b66\u80cc\u666f\u534a\u8def\u51fa\u5bb6\u5b66\u4e60\u6570\u5b66\u548c\u7269\u7406\u7684\u7279\u6b8a\u60c5\u51b5\u3002\u7ed3\u679c\u6070\u5de7\u5951\u5408\u4e86\u4e0a\u8ff0\u7684\u8fd9\u4e9b\u54c1\u5473\u3002\u5de5\u7a0b\u8bfe\u672c\u4f1a\u8ba9\u4f60\u76f8\u4fe1\u201c\u4f1a\u7b97\u624d\u61c2\uff0c\u61c2\u5c31\u662f\u4f1a\u7b97\uff0c\u4e0d\u4f1a\u7b97\u5c31\u662f\u4e0d\u61c2\u201d\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u8bfe\u672c\u7684\u6559\u5b66\u76ee\u6807\u662f\u5de5\u7a0b\u5e94\u7528\u3002\u4e0d\u4f1a\u7b97\uff0c\u61c2\u4e5f\u767d\u61c2\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6240\u8c13\u201c\u4f1a\u7b97\u201d\uff0c\u662f\u4e00\u79cd\u80a4\u6d45\u7684\u4f1a\u7b97\uff0c\u6240\u8c13\u201c\u4e0d\u4f1a\u7b97\u201d\uff0c\u5176\u5b9e\u66f4\u4f1a\u7b97\u3002\u4e4b\u6240\u4ee5\u4e0d\u8981\u540e\u8005\uff0c\u662f\u56e0\u4e3a\u5de5\u79d1\u6559\u80b2\u7684\u53d1\u5c55\uff0c\u5b66\u751f\u591a\u4e86\uff0c\u8d44\u8d28\u5e73\u5eb8\u4e86\uff0c\u6559\u5b66\u65f6\u95f4\u6709\u9650\u4e86\uff0c\u5404\u65b9\u9762\u8d44\u6e90\u9650\u5236\u90fd\u4e0d\u5141\u8bb8\u5b66\u751f\u904d\u5386\u62bd\u4ee3\u62d3\u6251\u5fae\u5206\u51e0\u4f55\u4e4b\u540e\u518d\u201c\u6740\u9e21\u7528\u725b\u5200\u201d\u5730\u53bb\u89e3\u51b3\u4e00\u4e9b\u4ee5\u5730\u7403\u4f5c\u53c2\u8003\u7cfb\u3001\u5bf9\u79f0\u5747\u8d28\u7684\u7b80\u5355\u95ee\u9898\u2014\u2014\u660e\u660e\u8bb0\u516c\u5f0f\u67e5\u8868\u5c31\u80fd\u529e\u5230\u3002<\/p>\n\n\n\n

Truesdell\u5728\u4e00\u672c\u4e66\u7406\u6027\u70ed\u529b\u5b66\u7684\u4e66\u4e2d\u4e5f\u8bf4\u8fc7\uff0c\u8981\u5c0a\u656c\u8fd9\u4e9b\u5de5\u7a0b\u5e08\u4eec\u3002\u4ed6\u4eec\u6b63\u5728\u505a\u7684\u4e8b\u60c5\u751a\u81f3\u5305\u62ec\u6d4b\u91cf\u4eba\u9020\u536b\u661f\u8868\u9762\u7684\u6e29\u5ea6\u3002\u5de5\u7a0b\u5e08\u4eec\u6d4b\u6e29\u5ea6\u7684\u60c5\u51b5\uff0c\u65e2\u4e0d\u662f\u5e73\u8861\u6001\uff0c\u4e5f\u4e0d\u662f\u51c6\u9759\u6001\u8fc7\u7a0b\uff0c\u4f46\u4ecd\u7136\u4f9d\u8d56\u5b83\u5b8c\u6210\u4e86\u5f88\u591a\u4f1f\u5927\u7684\u5de5\u4f5c\uff0c\u7136\u800c\u5728\u516c\u7406\u5316\u7684\u70ed\u529b\u5b66\u4e2d\u6e29\u5ea6\u662f\u5e73\u8861\u6001\u6982\u5ff5\u3002\u867d\u7136\u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770bTruesdell\u63d0\u51fa\u7684\u95ee\u9898\u4e0d\u662f\u4e00\u4e2a\u54f2\u5b66\u95ee\u9898\uff0c\u800c\u662f\u4e00\u4e2a\u53ef\u4ee5\u88ab\u7814\u7a76\u7684\u79d1\u5b66\u95ee\u9898\uff08\u8fdc\u79bb\u5e73\u8861\u6001\u4f53\u7cfb\u6709\u201c\u7b49\u6548\u6e29\u5ea6\u201d\uff09\uff0c\u4f46\u8fd9\u4e9b\u4e00\u822c\u89c2\u70b9\u8bf4\u660e\u4e86\uff0c\u5c31\u7b97\u8868\u9762\u4e0a\u73b0\u4ee3\u793e\u4f1a\u5df2\u7ecf\u627f\u8ba4\u201c\u79d1\u5b66\u5bf9\u6280\u672f\u7684\u5de8\u5927\u4f5c\u7528\u201d\uff0c\u4ece\u800c\u5728\u5de5\u7a0b\u5e08\u6559\u80b2\u4f53\u7cfb\u4e2d\u5f15\u5165\u4e86\u5927\u91cf\u73b0\u4ee3\u79d1\u5b66\u57fa\u7840\uff0c\u4f46\u5b9e\u9645\u4e0a\u5de5\u79d1\u6559\u80b2\u5e76\u6ca1\u6709\u6b63\u9762\u5730\u505a\u597d\u4efb\u4f55\u79d1\u5b66\u7684\u6559\u80b2\u3002\u751a\u81f3\u7531\u4e8e\u8fd9\u79cd\u6559\u80b2\u7684\u4ea7\u7269\u5145\u65a5\u5728\u4e86\u5b66\u672f\u5708\uff0c\u53e4\u5178\u610f\u4e49\u7684\u79d1\u5b66\u7814\u7a76\u53d7\u5230\u7684\u8bc4\u4ef7\u662f\u975e\u5e38\u8d1f\u9762\u7684\uff0c\u5c3d\u7ba1\u80cc\u540e\u7684\u54f2\u5b66\u4e5f\u662f\u975e\u5e38\u5de5\u5177\u7406\u6027\u7684\u3002\u4eba\u4eec\u6e10\u6e10\u5bf9\u4f5c\u4e3a\u7eaf\u7cbe\u795e\u6784\u5efa\u7684\u5b66\u672f\u7814\u7a76\u4e0d\u518d\u8010\u70e6\uff0c\u5bf9\u4e8e\u201c\u4ec5\u56e0\u4e3a\u666e\u9002\u7f8e\u800c\u975e\u8981\u7528\u725b\u5200\u6740\u9e21\u201d\u4e0d\u518d\u7406\u89e3\u3002<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

\u5728\u957f\u671f\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u6211\u5bf9\u4e00\u4ef6\u4e8b\u7684\u786e\u8ba4\u4e0d\u65ad\u5730\u5f3a\u5316\uff0c\u90a3\u5c31\u662f\u6211\u8ddfClifford Truesdell\u548cWalter Noll\u6709\u7740\u76f8\u540c\u7684\u201c\u54c1\u5473\u201d\u3002 \u6211\u8d5e\u540c\u5e76\u6b23\u8d4f\u5df2\u6709\u7269\u7406\u7406\u8bba\u7684\u516c\u7406\u5316\u52aa\u529b\u3002\u6211\u8ba4\u4e3a\u8fd9\u662f\u4e00\u4e2a\u6709\u610f\u4e49\u7684\u7814\u7a76\u9886\u57df\u3002\u6211\u5e0c\u671b\u6709\u4e00\u5929\u6211\u4eec\u7684\u672c\u79d1\u6559\u6750\u80fd\u66ff\u6362\u6210\u8fd9\u4e00\u9886\u57df\u7684\u7814\u7a76\u6210\u679c\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u5728\u6d41\u53d8\u5b66\u8bb2\u4e49\u4e2d\u5c31\u5c1d\u8bd5\u9075\u5faa\u4e00\u4e9b\u5df2\u7ecf\u5efa\u7acb\u7684\u516c\u7406\u5316\u5f15\u5165\u3002 \u6211\u7b2c\u4e00\u6b21\u770b\u5230Water Noll\u7684neo-classical space-time\u6784\u5efa\u662f\u5728\u4e0b\u9762\u8fd9\u4e2a\u5730\u65b9\uff1a W. Noll (1966), The Foundations of Mechanics, In: G. Grioli, C. Truesdell (eds), Non-linear Continuum Theories, Springer-Verlag \u8fd9\u4e66\u7684\u5370\u5237\u662f\u7528\u6253\u5b57\u673a\u7684\uff0c\u6709\u5f88\u82b1\u4f53notation\u662f\u540e\u9762\u518d\u7528\u624b\u5199\u8865\u4e0a\u7684\u3002\u6211\u4e0d\u77e5\u9053\u8fd9\u4e9b\u7b14\u8ff9\u662f\u4e0d\u662fNoll\u672c\u4eba\u7684\u3002\u4f46\u4ece\u6392\u7248\u4e0a\u53ef\u4ee5\u8bf4\u662f\u975e\u5e38\u4e0d\u53cb\u597d\u3002\u6211\u5bf9\u65f6\u7a7a\u6784\u5efa\u7684\u5185\u5bb9\u4e5f\u5b8c\u5168\u964c\u751f\u3002\u4f46\u662f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48\uff0c\u6211\u4e00\u5f00\u59cb\u5c31\u611f\u53d7\u5230\u8fd9\u4e2a\u8bdd\u9898\u662f\u5f88\u53ef\u80fd\u611f\u5174\u8da3\u7684\uff0c\u9b3c\u4f7f\u795e\u5dee\u5730\u628a\u5b83\u786c\u5543\u5b8c\u4e86\uff0c\u679c\u7136\u611f\u53d7\u5230\u4e86\u65e0\u6cd5\u7528\u8a00\u8bed\u5f62\u5bb9\u7684\u7f8e\u5b66\u4eab\u53d7\u3002\u9664\u4e86\u7f8e\u7684\u4eab\u53d7\u4e4b\u5916\uff0c\u65f6\u7a7a\u6784\u5efa\u7684\u4e25\u5bc6\u6027\uff0c\u53ef\u4ee5\u8ba9\u540e\u7eed\u7684\u5f88\u591a\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u5f53\u4e0b\u6559\u6750\u4e2d\u5bb9\u6613\u8ba9\u5b66\u751f\u641e\u6df7\u7684\u8bdd\u9898\u53d8\u5f97\u6839\u672c\u4e0d\u53ef\u80fd\u641e\u6df7\u3002 \u65e9\u671f\uff0c\u6211\u8865\u4e60\u6570\u5b66\u7684\u552f\u4e00\u53c2\u8003\u5c31\u662f S. Hassani (1999), Mathematical Physics: A Modern Introduction to Its Foundations, Springer 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\u540e\u6765\u6211\u4eceHassani\u7684\u4e66\u540e\u53c2\u8003\u4e66\u76ee\u53c8\u76f4\u63a5\u6216\u95f4\u63a5\u5730\u77e5\u9053\u4e86\u5f88\u591a\u4e66\u548c\u4f5c\u8005\u3002\u4f8b\u5982Halmos\u548c Hoffman and Kunze\u7684\u7ebf\u6027\u4ee3\u6570\u3002\u540e\u8005\u6210\u4e3a\u4e86\u6211\u7b2c\u4e00\u672c\u4e3b\u8981\u5b66\u4e60\u7684\u4e66\u3002Hoffman and Kunze\u5176\u5b9e\u662f\u4e00\u672c\u5904\u5904\u900f\u7740\u62bd\u8c61\u4ee3\u6570\u7684\u666e\u901a\u7ebf\u6027\u4ee3\u6570\uff0ccoordinate-free\u7684\u8272\u5f69\u66f4\u6d53\u4e86\u3002\u4e00\u4e2a\u8ba9\u6211\u66fe\u7ecf\u56f0\u60d1\uff0c\u5374\u53cd\u800c\u662f\u6781\u5176\u5177\u6709\u542f\u53d1\u6027\u7684\u7279\u70b9\u662f\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u7ebf\u6027\u4ee3\u6570\uff0c\u5168\u4e66\u6ca1\u6709\u201ccross product\u201d\u8fd9\u4e2a\u8bcd\u3002\u7ffb\u904d\u5168\u4e66\u53ea\u6709tensor product\u6ca1\u6709tensor\uff0c\u8fdb\u884ctensor product\u7684\u5bf9\u8c61\u53eb\u591a\u7ebf\u6027\u5f62\u5f0f\u3002\u73b0\u5728\u56de\u60f3\u8d77\u6765\uff0c\u6211\u6562\u8bf4\u5f88\u591a\u529b\u5b66\u8bfe\u7a0b\u7684\u8bb2\u8ff0\u8005\u4e0e\u8bb8\u672a\u5fc5\u80fd\u89e3\u7b54\u5b66\u751f\u5728\u4e00\u5207\u5176\u4ed6\u4e0d\u540c\u5730\u65b9\u770b\u5230\u7528\u201c\u5f20\u91cf\u201d\u4e8c\u5b57\u79f0\u547c\u7684\u5bf9\u8c61\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u4e1c\u897f\uff0c\u6709\u4ec0\u4e48\u8054\u7cfb\u3002 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Ferry\u7684\u7ecf\u5178\u6559\u6750\u3002\u4ed6\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relations between stress, strain, and their time dependences\u201d\u3002\u8fd9\u6bd4\u76f4\u63a5\u8bf4\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u591a\u4e86\u4e2a\u65f6\u95f4\u4f9d\u8d56\u6027\u3002\u8fd9\u5e76\u4e0d\u662f\u4e3a\u66f4\u51c6\u786e\u5730\u63cf\u8ff0\u672c\u6784\u5173\u7cfb\u7684\u610f\u4e49\u672c\u8eab\u4f5c\u51fa\u7684\u9650\u5b9a\uff0c\u800c\u662f\u4e3a\u4e86\u5f3a\u8c03\u6750\u6599\u7c98\u5f39\u6027\u7684\u53ef\u80fd\u6027\u3002\u6240\u4ee5\u5f52\u6839\u7ed3\u5e95\uff0c\u5728\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u8fd9\u4ef6\u4e8b\u4e0a\uff0c Ferry\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u4e86\u53e5\u201c\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u3002 Ferry\u7684\u4e66\u662f\u6d41\u4f20\u975e\u5e38\u5e7f\u7684\u3001\u53e3\u7891\u7ecf\u4e45\u4e0d\u8870\u7684\uff0c\u7ecf\u5178\u4e2d\u7684\u7ecf\u5178\u3002\u4f46\u662f\u4ed6\u5173\u4e8e\u672c\u6784\u5173\u7cfb\u7684\u7b80\u5355\u63cf\u8ff0\uff0c\u867d\u7136\u5fc5\u4e0d\u4ee3\u8868\u4ed6\u672c\u4eba\u7406\u89e3\u5c31\u771f\u8fd9\u4e48\u7b80\u5355\uff0c\u5374\u88ab\u8bb8\u591a\u4e5f\u8bb8\u53ea\u770b\u4e00\u672c\u4e66\u5b66\u6d41\u53d8\u5b66\uff0c\u8fd8\u5f88\u8ba4\u771f\u5b66\u7684\u5b66\u751f\u8bb0\u4e3a\u6559\u6761\u3002\u4f8b\u5982\uff0cM. Rao\u5199\u7684\u4e66\uff0c\u5c31\u539f\u6837\u7167\u642cFerry\u7684\u8bf4\u6cd5\uff0c\u5e76\u6807\u6ce8\u4e86\u5bf9Ferry\u7684\u4e66\u7684\u5f15\u7528\u3002 \u5982\u679c\u975e\u8981\u4fdd\u6301\u201c\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u201d\u8fd9\u79cd\u53d9\u8ff0\u6846\u67b6\u6765\u8bb2\u201c\u4f55\u8c13\u672c\u6784\u5173\u7cfb\u201d\u90a3\u81f3\u5c11\u5e94\u8be5\u52a0\u4ec0\u4e48\u6837\u7684\u9650\u5b9a\u6027\u8bf4\u660e\u5462\uff1f\u4e24\u65b9\u9762\u3002\u4e00\u662f\uff0c\u6240\u8c13\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u5f20\u91cf\uff0c\u5b83\u4eec\u6bcf\u4e2a\u67099\u4e2a\u91cf\u3002\u4f46\u8fd9\u4ef6\u4e8b\u8981\u4ee5\u4e0d\u51fa\u73b0\u201c\u5f20\u91cf\u201d\u8fd9\u4e2a\u6982\u5ff5\u7684\u65b9\u5f0f\u8bf4\u51fa\u6765\uff0c\u8ba9\u4eba\u4e00\u4e0b\u5b50\u5c31\u660e\u767d\u4e3a\u4ec0\u4e48\u5b83\u4eec\u662f\u8fd9\u79cd\u91cf\uff0c\u81f3\u5c11\u53cd\u6b63\u4e0d\u662f\u6807\u91cf\uff08\u5f88\u96be\uff09\uff1b\u4e8c\u662f\uff0c\u5e94\u529b\u548c\u5e94\u53d8\u90fd\u662f\u573a\uff0c\u5b83\u4eec\u7684\u201c\u53d6\u503c\u201d\u65e2\u4f9d\u8d56\u7a7a\u95f4\u4f4d\u7f6e\u53c8\u4f9d\u8d56\u65f6\u95f4\u3002\u8fd9\u5012\u4e0d\u662f\u4ec0\u4e48\u5f88\u96be\u7406\u89e3\u7684\u70b9\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u90fd\u660e\u786e\u4e86\uff0c\u90a3\u5c31\u53ef\u4ee5\u6210\u529f\u7684\u8ba9\u4eba\u5bf9\u201c\u65cb\u8f6c\u6d41\u53d8\u4eea\u8f6f\u4ef6\u6240\u8f93\u51fa\u7ed9\u4f60\u7684\u6807\u91cf\u503c\u5e94\u529b\u548c\u5e94\u53d8\u5230\u5e95\u662f\u5565\u201d\u4ea7\u751f\u8d28\u7591\uff1b\u8fd9\u4e2a\u8d28\u7591\u624d\u662f\u6b63\u5f0f\u5b66\u4e60\u6d41\u53d8\u5b66\u7684\u5f00\u7aef\u2014\u2014\u5982\u679c\u4f60\u6070\u5de7\u5c31\u662f\u90a3\u79cd\u6ca1\u5b66\u6d41\u53d8\u5b66\u5c31\u7167\u7740\u6587\u732e\u6216\u5e08\u5144\u5e08\u59d0\u7684\u201c\u6307\u5bfc\u201d\u505a\u4e86\u5927\u91cf\u65cb\u8f6c\u6d41\u53d8\u4eea\u5b66\u6d4b\u8bd5\u7684\u5b66\u751f\u7684\u8bdd\u3002 1.1 \u5e94\u529b\u3001\u5e94\u53d8\u90fd\u662f\u573a\u51fd\u6570 \u6211\u4eec\u5148\u770b\u6697\u793a\u4e86\u7b2c\u4e8c\u4e2a\u70b9\u7684\u8bf4\u6cd5\u3002 \u6709\u672c\u4e66Yamaguchi (2008)\u8bf4\u672c\u6784\u5173\u7cfb\u662f\u201cthe relationship between the internal stress and the applied strain\u201d\uff0c\u8fd9\u4e2a\u201cinternal\u201d\u5c31\u5f88\u9e21\u8d3c\u3002\u4e0d\u5c31\u662f\u60f3\u6697\u6233\u6233\u5730\u5f3a\u8c03\u4e00\u4e0b\u201c\u5b83\u4eec\u90fd\u662f\u573a\u54e6\u201d\u5417\uff1f \u8fd8\u6709\u4e00\u672c\u4e66Mewis & Wagner (2012)\u8bf4\uff0c\u672c\u6784\u5173\u7cfb\u662f\u201cintrinsic relation between the stresses and kinematics\u201d\u3002\u5728\u672c\u5173\u6ce8\u7126\u70b9\u4e0b\uff0c\u8fd9\u53e5\u8bdd\u65e0\u975e\u7ed9\u4f60\u6765\u4e86\u4e2a\u201ckinematics\u201d\u8fd9\u8bcd\uff0c\u597d\u50cf\u8bf4\u5f97\u60ac\u4e00\u70b9\u513f\uff0c\u80fd\u8ba9\u4f60\u4e0d\u6562\u786e\u5b9a\u4f5c\u8005\u662f\u4e0d\u662f\u80a4\u6d45\u7684\u3002 \u7c7b\u4f3c\u4e0a\u8ff0\u8fd9\u822c\u7684\u201c\u514d\u8d23\u5f0f\u201d\u7684\u4fee\u9970\u9650\u5b9a\uff0c\u5bf9\u521d\u5b66\u8005\u66f4\u51c6\u786e\u5730\u7406\u89e3\u4e00\u70b9\u7528\u5904\u90fd\u6ca1\u6709\uff1b\u5728\u521d\u5b66\u8005\u90a3\u91cc\u4e0a\u8ff0\u8fd9\u79cd\u505a\u6cd5\u76f8\u5f53\u4e8e\u7b80\u5355\u8bf4\u672c\u6784\u5173\u7cfb\u5c31\u662f\u5e94\u529b\u5e94\u53d8\u5173\u7cfb\u3002 1.2 \u5e94\u529b\u3001\u5e94\u53d8\u662f\u5f20\u91cf\uff08\u4f46\u4e0d\u660e\u8bf4\uff09 \u5728\u4e00\u53e5\u8bdd\u4e2d\u4e0d\u660e\u8bf4\u5f20\u91cf\u53c8\u5f3a\u8c03\u51fa\u8fd9\u4e00\u610f\u4e49\u7684\u96be\u5ea6\u786e\u5b9e\u6709\u70b9\u513f\u5927\u3002\u6211\u53cd\u6b63\u662f\u505a\u4e0d\u5230\u7684\u3002\u6211\u7ffb\u7684\u4e66\uff0c\u6709\u5f88\u591a\u4e5f\u505a\u4e0d\u5230\u3002\u6240\u4ee5\u5b9e\u9645\u4e0a\u5f88\u591a\u4e66\u5e72\u8106\u5728\u53e5\u5b50\u4e2d\u51fa\u73b0\u201c\u5f20\u91cf\u201d\u8fd9\u8bcd\u4e86\u3002\u5728\u8fd9\u4e9b\u4e66\u5f53\u4e2d\uff0c\u6709\u4e9b\u662f\u5728\u4ecb\u7ecd\u5b8c\u5e94\u529b\u5f20\u91cf\u4e4b\u524d\u5c31\u8bb2\u672c\u6784\u5173\u7cfb\u662f\u4ec0\u4e48\u7684\u8bdd\uff0c\u6240\u4ee5\u201c\u5f20\u91cf\u201d\u4e00\u8bcd\u7684\u51fa\u73b0\u662f\u63d0\u524d\u7684\u3002\u800c\u4e14\u4e00\u4e9b\u5c31\u662f\u5230\u4e86\u8bb2\u672c\u6784\u65b9\u7a0b\u7684\u90e8\u5206\u624d\u8bf4\u4ec0\u4e48\u662f\u672c\u6784\u5173\u7cfb\uff0c\u4f46\u8fd9\u79cd\u60c5\u51b5\u4e0b\u672c\u6587\u5173\u6ce8\u7684\u95ee\u9898\u5c31\u4e0d\u5b58\u5728\u4e86\uff0c\u56e0\u4e3a\u90fd\u5230\u4e86\u8bb2\u672c\u6784\u65b9\u7a0b\u7684\u7ae0\u8282\u4e86\uff0c\u90a3\u5e94\u529b\u5f20\u91cf\u3001\u8fd0\u52a8\u5b66\u3001\u5b88\u6052\u5f8b\u3001\u8fd0\u52a8\u65b9\u7a0b\u7b49\u77e5\u8bc6\u5e94\u8be5\u90fd\u8bb2\u8fc7\u4e86\u3002\u2026","rel":"","context":"In "\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0"","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8206,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8206","url_meta":{"origin":8305,"position":1},"title":"\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u5386\u53f2\uff08\u4e00\uff09","author":"Andrew","date":"2021\u5e748\u670816\u65e5","format":false,"excerpt":"\u524d\u6bb5\u65f6\u95f4\u505a\u8fc7\u4e00\u4e9b\u5173\u4e8e\u7c98\u5f39\u6027\uff08viscoelasticity\uff09\u7684\u7814\u7a76\u5386\u53f2\u7684\u8d44\u6599\u8c03\u67e5\uff0c\u5c31\u5728\u6b64\u4f5c\u4e00\u4e9b\u4e0d\u5b8c\u6574\u7684\u603b\u7ed3\u3002 \u5b9e\u9645\u4e0aMaria Grazia Ianniello\u4f5c\u4e86\u5f88\u597d\u7684\u603b\u7ed3\u5de5\u4f5c\u200b(Ianniello 1993)\u200b\u200b*\u200b\uff0c\u6211\u5199\u7684\u5185\u5bb9\u5927\u90e8\u5206\u90fd\u662f\u76f4\u63a5\u6765\u81ea\u8fd9\u91cc\u3002\u5176\u5b9e\u6211\u4e5f\u72ec\u7acb\u5730\u8bc4\u4f30\u8fc7\u5979\u7684\u8bba\u6587\u3002\u6211\u81ea\u5df1\u770b\u8fc7\u4e00\u90e8\u5206\u7684\u5386\u53f2\u6587\u732e\u7684\u539f\u6587\uff08\u89c1\u6b64\u6587\uff09\uff0c\u518d\u53bb\u770bIanniello\u5bf9\u8fd9\u4e9b\u539f\u6587\u7684\u89e3\u8bfb\uff0c\u89c9\u5f97\u5979\u5173\u6ce8\u7ec6\u8282\u8ddf\u6211\u4e00\u6837\u591a\uff0c\u751a\u81f3\u770b\u5f97\u548c\u60f3\u5f97\u6bd4\u6211\u66f4\u4ed4\u7ec6\u3002\u79d1\u5b66\u54f2\u5b66\u5c42\u9762\u4e0a\u7684\u5173\u7167\u89d2\u5ea6\u4e5f\u548c\u6211\u5f88\u63a5\u8fd1\uff0c\u56e0\u6b64\u6211\u5f88\u4fe1\u8d56\u8fd9\u4e2a\u5de5\u4f5c\u3002\u53e6\u5916\u8fd8\u6709\u4e00\u7bc7\u66f4\u65e9\u4e9b\u7684\u79d1\u5b66\u53f2\u8bba\u6587\u200b(D\u00f6rries 1991)\u200b\uff0c\u4ece\u5e7f\u4e49\u7684\u201c\u4f59\u6548\u201d\uff08Nachwirking\uff09\u4e0e\u201c\u8fdf\u6ede\u201d\uff08histeresis\uff09\u6982\u5ff5\u7684\u89d2\u5ea6\u56de\u987e\u4e8619\u4e16\u7eaa\u7684\u7269\u7406\u5b66\u53f2\uff0c\u4f46\u662f\u63cf\u8ff0\u4e0d\u5982Ianniello\u7684\u6587\u7ae0\u8be6\u7ec6\u3002\u9664\u4e86\u8fd9\u4e9b\u79d1\u5b66\u53f2\u7814\u7a76\u8005\u7684\u8bba\u6587\u5916\uff0c\u6211\u5728\u8fd9\u91cc\u63d0\u4e00\u4e9b\u6d41\u53d8\u5b66\u5bb6\u81ea\u5df1\u505a\u7684\u5386\u53f2\u603b\u7ed3\u3002\u200b(Tanner and Walters 1998)\u200b\u7684\u8fd9\u672c\u4e66\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u4e00\u4e2a\u5927\u7684\u5386\u53f2\u603b\u7ed3\uff0c\u662f\u4e00\u4e2a\u5f88\u4f1f\u5927\u7684\u5de5\u7a0b\uff0c\u4f46\u662f\u96be\u514d\u4e5f\u6d41\u4e8e\u6cdb\u6cdb\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u7c97\u7565\u7684\u63d0\u7eb2\u548c\u53c2\u8003\u6587\u732e\u6765\u53c2\u8003\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cHershel Markovitz\u505a\u8fc7\u7684\u5f88\u591a\u6d41\u53d8\u5b66\u53f2\u603b\u7ed3\u66f4\u52a0\u95ee\u9898\u5bfc\u5411\u56e0\u800c\u4e5f\u66f4\u5bcc\u6709\u6d1e\u89c1\u200b(Markovitz 1968, 1977, 1985)\u200b\u3002\u200b(Doraiswamy 2002)\u200b\u4e5f\u505a\u4e86\u4e00\u4e2a\u5f88\u5168\u9762\u7684\u5386\u53f2\u6eaf\u6e90\u8d44\u6599\u603b\u7ed3\u3002\u200b(Tanner 2002)\u200b\u603b\u7ed3\u4e86\u6d41\u53d8\u6d4b\u91cf\u5b66\u4e2d\u6b63\u5f26\u6d4b\u8bd5\u65b9\u6cd5\u7684\u5386\u53f2\u3002 \u5df2\u6545\u7684\u6d41\u53d8\u5b66\u5bb6\u90d1\u878d\u8001\u5e08\u5728\u79d1\u5b66\u7f51\u4e0a\u7684\u535a\u5ba2\u5199\u6ee1\u4e86\u810d\u7099\u4eba\u53e3\u7684\u6d41\u53d8\u5b66\u53f2\u8bdd\u3002 1. \u4eca\u5929\u77e5\u9053\u7684\u201c\u7c98\u5f39\u6027\u201d \u201c\u7c98\u5f39\u6027\u201d\uff08viscoelasticity\uff09\u662f\u6d41\u53d8\u5b66\u6216\u529b\u5b66\u65b9\u9762\u7684\u8bcd\u3002 Ferry\u5bf9\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u5b8f\u89c2\u552f\u8c61\u7406\u8bba\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u8fdb\u884c\u4e86\u5b8c\u6574\u7684\u603b\u7ed3\u200b(Ferry 1980)\u200b\u3002\u800c\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u5c31\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u5176\u73b0\u8c61\u5b66\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u53ef\u89c1\u4e8e\u5404\u4e2a\u6d41\u53d8\u5b66\u6559\u6750\u3002\u503c\u63d0\u4e00\u63d0\u7684\u662f\u632f\u8361\u6d4b\u8bd5\u5728\u975e\u7ebf\u6027\u54cd\u5e94\u4e2d\u7684\u63cf\u8ff0\u6846\u67b6\u5728\u6d41\u53d8\u5b66\u4e2d\u7684\u5e94\u7528\u662f\u201c\u5927\u5e45\u632f\u8361\u526a\u5207\u201d\uff08large amplitude oscillatory shear\uff0cLAOS\uff09\u3002\u8fd9\u65b9\u9762\u6700\u8fd1\u7684\u5927\u578b\u7efc\u8ff0\u200b(Hyun et al. 2011)\u200b\u5df2\u7ecf\u5f88\u65e9\u4e86\uff0c\u5176\u4e4b\u540e\u503c\u5f97\u5173\u6ce8\u7684\u76f8\u5173\u7efc\u8ff0\u6709\u200b(Bird and Giacomin 2016)\u200b\u548c\u200b(Voigtmann 2014)\u200b\u3002 \u4e8b\u5b9e\u4e0a\u7c98\u5f39\u6027\u7684\u73b0\u8c61\u5728\u529b\u5b66\u4e4b\u5916\u6709\u66f4\u4e00\u822c\u7684\u672c\u8d28\uff0c\u5b83\u5b9e\u8d28\u4e0a\u662f\u4e00\u79cd\u677e\u5f1b\uff08\u5f1b\u8c6b\uff09\u73b0\u8c61\u200b\u2020\u200b\uff0c\u5728\u7535\u78c1\u5b66\u4e2d\u4e5f\u5f88\u666e\u904d\u3002\u56e0\u6b64Oppenheim\u7684\u7ecf\u5178\u6559\u79d1\u4e66\u200b(Oppenheim et al. 1997)\u200b\u4e2d\u7684\u5f88\u591a\u65b9\u6cd5\u8ddf\u7c98\u5f39\u6027\u73b0\u8c61\u5b66\u662f\u76f8\u901a\u7684\u3002\u4f8b\u5982\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u901a\u7528\u672c\u6784\u2014\u2014Boltzmann\u65b9\u7a0b\u5c31\u662f\u4e00\u4e2a\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf\u7684\u5377\u79ef\u5f0f\u3002\u5728\u540e\u9762\u7684\u5386\u53f2\u4ecb\u7ecd\u4e2d\u6211\u4eec\u5c06\u4f1a\u770b\u5230\uff0c\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u53f2\u8ddf\u7535\u78c1\u5b66\u548c\u7535\u4fe1\u6280\u672f\u7684\u53d1\u5c55\u662f\u5bc6\u5207\u76f8\u5173\u7684\u3002\u4e00\u9886\u57df\u7684\u6982\u5ff5\u6216\u65b9\u6cd5\u5ef6\u7528\u4e8e\u53e6\u4e00\u9886\u57df\u7684\u60c5\u51b5\u5f88\u5e38\u89c1\uff0c\u4e14\u8fd9\u79cd\u60c5\u51b5\u4e00\u76f4\u5ef6\u7eed\u5230\u4eca\u5929\u3002 \u81f3\u4e8e\u5b8f\u89c2\u7c98\u5f39\u6027\u6216\u5176\u4ed6\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\uff0c\u5219\u662f\u975e\u5e73\u8861\u6001\u7edf\u8ba1\u529b\u5b66\u63d0\u4f9b\u7684\u3002\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u8bf4\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\u5c31\u662f\u70ed\u8fd0\u52a8\u3002\u5177\u4f53\u5730\uff0c\u7ebf\u6027\u54cd\u5e94\u7406\u8bba\u662f\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7edf\u8ba1\u57fa\u7840\u3002\u8fd9\u65b9\u9762\u5185\u5bb9\u53ef\u4ee5\u53c2\u8003\u200b(Evans and Morriss 2008)\u200b\u548c\u200b(Kreuzer 1981)\u200b\u3002 \u4e0a\u8ff0\u5f15\u7528\u7684\u8d44\u6599\u4ee3\u8868\u4e86\u6211\u4eec\u4eca\u5929\u5bf9\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u3002\u5728\u56de\u987e\u7c98\u5f39\u6027\u7684\u7814\u7a76\u5386\u53f2\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5c31\u81ea\u7136\u4f1a\u5173\u6ce8\u5f53\u65f6\u7684\u4eba\u4ece\u5f53\u65f6\u7684\u6570\u5b66\u548c\u7269\u7406\u5b66\u57fa\u7840\u548c\u5b9e\u9a8c\u73b0\u8c61\u6240\u80fd\u5f62\u6210\u7684\u6700\u521d\u8ba4\u8bc6\u8ddf\u4eca\u5929\u8ba4\u8bc6\u7684\u5dee\u5f02\u548c\u5dee\u8ddd\u662f\u600e\u6837\u7684\uff1f\u4e4b\u540e\u662f\u5982\u4f55\u201c\u677e\u5f1b\u201d\u5230\u4eca\u5929\u7684\u8ba4\u8bc6\u7684\uff1f 2. \u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e0e\u70ed\u529b\u5b66 \u6211\u4eec\u4eca\u5929\u7684\u8ba4\u8bc6\u4f53\u7cfb\u4e2d\uff0c\u7c98\u5f39\u6027\u73b0\u8c61\u662f\u5bf9\u7ecf\u5178\u7684\u864e\u514b\u5f39\u6027\u548c\u725b\u987f\u7c98\u6027\u7684\u63a8\u5e7f\u3002\u4ece\u66f4\u5927\u7684\u89d2\u5ea6\u770b\uff0c\u7c98\u5f39\u6027\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e2d\u7684\u7279\u6b8a\u672c\u6784\u5173\u7cfb\u3002\u4eca\u5929\u5982\u679c\u6211\u4eec\u8981\u8bb2\u8ff0\u7c98\u5f39\u6027\uff0c\u6211\u4eec\u4f1a\u5e0c\u671b\u542c\u4f17\u5df2\u7ecf\u5bf9\u4e0a\u8ff0\u8fd9\u4e9b\u80cc\u666f\u6709\u6240\u4e86\u89e3\u200b\u2021\u200b\u3002 \u9996\u5148\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u3002\u6b27\u62c9\u628a\u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b\u63a8\u5e7f\u81f3\u8fde\u7eed\u4ecb\u8d28\uff0c\u5e76\u63a8\u5bfc\u4e86\u521a\u4f53\u548c\u7406\u60f3\u6d41\u4f53\u7684\u65b9\u7a0b\u200b(Truesdell 1960a, 1968)\u200b\u200b\u00a7\u200b\u3002\u8fd9\u5927\u6982\u662f\u5341\u516b\u4e16\u7eaa\u4e2d\u53f6\u7684\u4e8b\u60c5\u3002 \u5173\u4e8e\u80fd\u91cf\u5b88\u6052\uff0c\u4e5f\u8bb8\u4f2f\u52aa\u5229\u7684\u5de5\u4f5c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u79cd\u4ee3\u8868\uff0c\u4ee5\u4ed61738\u5e74\u53d1\u8868\u7684Hydrodynamica\u4e3a\u6807\u5fd7\u200b(Truesdell 1960a, 1968)\u200b\u3002\u4f2f\u52aa\u5229\u65b9\u7a0b\uff0c\u5c31\u662f\u673a\u68b0\u80fd\u4e0e\u91cd\u529b\u52bf\u80fd\u4e4b\u95f4\u7684\u80fd\u91cf\u5b88\u6052\u3002\u4ec5\u8003\u8651\u8fd9\u4e24\u79cd\u80fd\u91cf\u4e4b\u95f4\u7684\u5b88\u6052\u662f\u7ecf\u5178\u529b\u5b66\u53d1\u5c55\u8fc7\u7a0b\u4e2d\u7684\u4e00\u4e2a\u4e3b\u8981\u7684\u95ee\u9898\u5f62\u5f0f\u3002\u70ed\u529b\u5b66\u610f\u4e49\u4e0a\u7684\u80fd\u91cf\u5b88\u6052\uff08\u5373\u4f5c\u4e3a\u516c\u8bbe\u7684\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\uff09\uff0c\u5219\u4e0e\u70ed\u7684\u672c\u8d28\u95ee\u9898\u548c\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u8ba4\u8bc6\u7b49\u4e00\u540c\u7ea0\u7f20\u523019\u4e16\u7eaa\u4e2d\u671f\u624d\u7b97\u786e\u7acb\u3002\u2026","rel":"","context":"In "\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0"","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8720,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8720","url_meta":{"origin":8305,"position":2},"title":"\u5206\u4eab\u4e00\u4e9b\u4e66\uff081\uff09","author":"Andrew","date":"2022\u5e7412\u67086\u65e5","format":false,"excerpt":"\u4e00\u3001 \u6211\u8ba4\u4e3a\uff08\u5e7f\u4e49\u7684\uff09\u5316\u5b66\u4e13\u4e1a\u7684\u5b66\u751f\u6709\u5fc5\u8981\u5b66\u4e60\u6bd4\u73b0\u5728\u7684\u6559\u5b66\u4f53\u7cfb\u4e2d\u6240\u542b\u6709\u7684\u591a\u5f97\u591a\u7684\u6570\u5b66\u548c\u7269\u7406\u3002\u56e0\u4e3a\uff0c\u5f88\u591a\u7269\u7406\u5b66\u9886\u57df\u6216\u95ee\u9898\uff0c\u4eca\u65f6\u4eca\u65e5\u53ea\u6709\u5316\u5b66\u5bb6\u4eec\u5173\u5fc3\u4e86\u3002\u8fd9\u4e9b\u9886\u57df\u5728\u7269\u7406\u5b66\u754c\u5df2\u7ecf\u4e0d\u53d7\u91cd\u89c6\uff0c\u6216\u8005\uff0c\u505a\u8fd9\u4e9b\u9886\u57df\u7684\u7269\u7406\u5b66\u5bb6\u6e10\u6e10\u88ab\u8ba4\u4e3a\u662f\u5316\u5b66\u5bb6\u3002\u4f46\u662f\u4ece\u6559\u5b66\u80cc\u666f\u4e0a\uff0c\u80fd\u505a\u5f97\u52a8\u8fd9\u4e9b\u9886\u57df\u7814\u7a76\u7684\u4eba\uff0c\u4ecd\u7136\u662f\u7269\u7406\u7cfb\u80cc\u666f\u7684\u4e3a\u4e3b\u3002\u4ee5\u5316\u7c7b\u4e13\u4e1a\u76ee\u524d\u7684\u6559\u5b66\u4f53\u7cfb\uff0c\u4e0d\u5927\u91cf\u8865\u4e60\u5fc5\u8981\u7684\u6570\u5b66\u548c\u7269\u7406\u77e5\u8bc6\u662f\u505a\u4e0d\u52a8\u8fd9\u4e9b\u9886\u57df\u7684\u95ee\u9898\u7684\uff0c\u751a\u81f3\u7406\u89e3\u4e0d\u4e86\u3002 \u6211\u8ba4\u4e3a\uff0c\u65e2\u7136\u53ea\u6709\u5316\u5b66\u5bb6\u5173\u5fc3\u8fd9\u4e9b\u9886\u57df\uff0c\u90a3\u8fd9\u4e9b\u9886\u57df\u5c31\u4e0d\u8be5\u89c6\u4e3a\u7269\u7406\u5b66\u9886\u57df\u2014\u2014\u65e0\u8bba\u5b83\u591a\u4e48\u201c\u50cf\u4e00\u95e8\u7269\u7406\u201d\u3002\u4ece\u8fd8\u539f\u8bba\u7684\u89c2\u70b9\uff0c\u6240\u6709\u81ea\u7136\u79d1\u5b66\u90fd\u662f\u7269\u7406\u5b66\u3002\u5982\u679c\u8bf4\u8fd9\u79cd\u8bba\u8c03\u662f\u65e0\u804a\u7684\uff0c\u90a3\u6211\u4eec\u5c31\u53ea\u5269\u4e0b\u6839\u636e\u201c\u8c01\u5173\u5fc3\u4ec0\u4e48\u9886\u57df\u201d\u8fd9\u4ef6\u4e8b\u4e0a\u7684\u4e00\u4e9b\u5171\u6027\u6765\u5212\u5206\u5b66\u79d1\u4e86\u4f8b\u5982\uff0c\u5316\u5b66\u5bb6\u5982\u679c\u5173\u5fc3\u5230\u4e86\u751f\u7269\u4e00\u4e9b\u95ee\u9898\uff0c\u90a3\u8fd9\u4e9b\u95ee\u9898\u5c31\u662f\u5316\u5b66\u95ee\u9898\uff0c\u5728\u8fd9\u4e9b\u95ee\u9898\u4e0a\u7684\u6210\u5c31\u5982\u679c\u80fd\u83b7\u5f97\u8bfa\u8d1d\u5c14\u5956\uff0c\u90a3\u5e94\u8be5\u5c5e\u4e8e\u8bfa\u8d1d\u5c14\u5316\u5b66\u5956\u2014\u2014\u6b63\u5982\u5b9e\u9645\u4e0a\u8fc7\u53bb\u597d\u591a\u5e74\u7684\u8bfa\u8d1d\u5c14\u5316\u5b66\u5c06\u90a3\u6837\uff08\u5c3d\u7ba1\u5f88\u591a\u4eba\u5e76\u4e0d\u4e70\u5e10\uff0c\u8ba4\u4e3a\u90fd\u662f\u751f\u7269\u5b66\u7684\u5de5\u4f5c\uff09\u3002 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\u4e94\u3001 \u5f88\u591a\u9762\u5411\u7269\u7406\u7cfb\u5b66\u751f\u7684\u201c\u6570\u5b66\u7269\u7406\u65b9\u6cd5\u201d\u8bfe\u672c\uff0c\u662fanti-mathematics\u7684\u3002\u5b83\u4eec\u4e0d\u8fc7\u662f\u4e00\u4e2a\u7a0d\u5fae\u6269\u5927\u4e86\u7684\u201c\u6570\u5b66\u51c6\u5907\u201d\uff0c\u662f\u201c\u4f1a\u7b97\u5c31\u884c\u201d\u90aa\u6559\u4ea7\u7269\u3002\u56e0\u6b64\u6211\u4e0d\u5efa\u8bae\u7eaf\u6d01\u7684\u5316\u5b66\u4e13\u4e1a\u5b66\u751f\u627e\u8fd9\u7c7b\u4e66\u6765\u5b66\u4e60\u6570\u5b66\u3002\u4f46\u9664\u4e86\u4e00\u672c\uff1a Sadri Hassani (2003), Mathematical Physics: A Modern Introduction to Its Foundations, 2nd ed., Springer 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