{"id":30902,"date":"2018-05-08T10:59:00","date_gmt":"2018-05-08T02:59:00","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=30902"},"modified":"2018-07-29T19:34:55","modified_gmt":"2018-07-29T11:34:55","slug":"%e6%88%91%e7%8c%9c%e7%89%9b%e9%a0%93%e6%98%af%e9%80%99%e6%a8%a3%e5%be%97%e5%88%b0%e7%ac%ac%e4%b8%89%e9%81%8b%e5%8b%95%e5%ae%9a%e5%be%8b","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=30902","title":{"rendered":"\u6211\u731c\u725b\u9813\u662f\u9019\u6a23\u5f97\u5230\u7b2c\u4e09\u904b\u52d5\u5b9a\u5f8b"},"content":{"rendered":"<p><strong>\u64b0\u6587\uff5c\u8d99\u5149\u5b89\u6559\u6388<\/strong><\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u524d\u8a00<\/strong><\/span><\/p>\n<p>\u6211\u5728\u9ad8\u96c4\u4e2d\u5b78\u9ad8\u4e2d\u4e09\u5e74\u7d1a\u7684\u7269\u7406\u8ab2\u662f\u5f9e\u529b\u5b78\u958b\u59cb\uff1a\u725b\u9813\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\uff0c\u725b\u9813\u7684\u4e09\u500b\u904b\u52d5\u5b9a\u5f8b\uff0c\u864e\u514b\u5b9a\u5f8b\uff0c\u2026 \u7b49\u7b49\u3002\u6211\u66fe\u7d93\u81ea\u5275\u4e00\u500b\u201c\u8868\u9762\u7c97\u7cd9\u6a21\u578b\u201d\uff0c\u61c9\u7528\u725b\u9813\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\uff0c\u63a8\u5c0e\u51fa\u4f86\u864e\u514b\u5b9a\u5f8b\uff0c\u65bc\u662f\u66f4\u60f3\u77e5\u9053\u725b\u9813\u662f\u5982\u4f55\u767c\u73fe\u9019\u4e9b\u91cd\u8981\u5b9a\u5f8b\u3002\u96d6\u7136\u6211\u662f\u832b\u7121\u982d\u7dd2\uff0c\u6211\u7684\u7269\u7406\u8001\u5e2b\u80e1\u5b87\u5e73\u4e5f\u4e0d\u80fd\u7d66\u6211\u7b54\u6848\uff0c\u4ed6\u537b\u9f13\u52f5\u6211\u4e0d\u8981\u653e\u68c4\u3002<\/p>\n<p>\u904e\u53bb\u5e7e\u5341\u5e74\u4e2d\uff0c\u65b7\u65b7\u7e8c\u7e8c\u7684\u5076\u723e\u60f3\u5230\u9019\u56de\u4e8b\u3002\u4f86\u5230\u6b50\u6d32\u4ee5\u5f8c\uff0c\u5f97\u5229\u65bc\u5929\u6642\u3001\u5730\u5229\u3001\u4eba\u548c\uff0c\u7d42\u65bc\u6478\u7d22\u51fa\u4e00\u4e9b\u982d\u7dd2\u3002\u4e0d\u4e45\u524d\u6574\u7406\u4e86\u4e00\u7bc7\u6f14\u8b1b\u7a3f\uff0c\u6558\u8ff0\uff08\u6211\u8a8d\u70ba\uff09\u725b\u9813\u767c\u73fe\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u7684\u601d\u7dad\u904e\u7a0b\uff0c\u5f97\u5230\u4e86\u4ee5\u4e0b\u7684\u7d50\u679c\u3002\u4ee4\u592a\u967d\u7684\u8cea\u91cf\u70ba M\uff0c\u5730\u7403\u7684\u8cea\u91cf\u70ba m\uff0c\u592a\u967d\u8207\u5730\u7403\u7684\u8ddd\u96e2\u70ba R\u3002\u6211\u63a8\u8ad6\u51fa\uff1a\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\u662f F<sub>M<\/sub>(m) \u221e C(M)m\/R<sup>2<\/sup>, \u6b64\u8655\u7684 C(M) \u53ea\u548c\u592a\u967d\u7684\u8cea\u91cf M \u6709\u95dc\u3002\u7576\u7136\uff0c\u5730\u7403\u5c0d\u592a\u967d\u7684\u5f15\u529b\u662f F<sub>m<\/sub>(M) \u221e C(m)M\/R<sup>2<\/sup>, \u6b64\u8655\u7684 C(m) \u53ea\u548c\u5730\u7403\u7684\u8cea\u91cf m \u6709\u95dc\u3002\u4f46\u662f\u6211\u4e0d\u660e\u767d\u725b\u9813\u662f\u5982\u4f55\u5f97\u5230\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u00a0 F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\uff0c\u6b64\u8655\u7684 C \u53ea\u662f\u4e00\u500b\u5e38\u6578\u3002<\/p>\n<p>\u5f8c\u4f86\u6211\u53c8\u5beb\u4e86\u4e00\u7bc7\u624b\u7a3f\uff0c\u6558\u8ff0\uff08\u6211\u8a8d\u70ba\uff09\u725b\u9813\u5982\u4f55\u5f97\u5230\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\uff0c\u4f46\u662f\u6211\u59cb\u7d42\u641e\u4e0d\u61c2\u725b\u9813\u5982\u4f55\u5f97\u5230\u7b2c\u4e09\u904b\u52d5\u5b9a\u5f8b\u3002\u7b2c\u4e09\u5b9a\u5f8b\u898f\u7bc4\u4e86\u5169\u500b\u7269\u9ad4\u76f8\u4e92\u4f5c\u7528\u6642\uff0c\u4f5c\u7528\u529b\u548c\u53cd\u4f5c\u7528\u529b\u7684\u95dc\u4fc2\uff0c\u53ef\u662f\u5169\u500b\u7269\u9ad4\u7684\u76f8\u4e92\u4f5c\u7528\u53ef\u4ee5\u662f\u63a5\u89f8\u7684\uff0c\u4e5f\u53ef\u4ee5\u662f\u975e\u63a5\u89f8\u7684\uff0c\u5fc5\u9808\u5206\u5225\u8a0e\u8ad6\u3002\u73fe\u5728\u6211\u8a66\u5716\u63a8\u8ad6 F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\uff0c\u7136\u5f8c\u548c\u725b\u9813\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\u7d50\u5408\u8d77\u4f86\uff0c\u5f97\u5230\u725b\u9813\u7b2c\u4e09\u904b\u52d5\u5b9a\u5f8b\u3002<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5169\u500b\u7269\u9ad4\u4e4b\u9593\u7684\u300c\u975e\u63a5\u89f8\u300d\u76f8\u4e92\u4f5c\u7528<\/strong><\/span><\/p>\n<p>\u725b\u9813\u7684\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u662f\u5efa\u7acb\u5728\u4e00\u500b\u300c\u8cea\u9ede\u6a21\u578b\u300d\u4e0a\u7684\u3002\u592a\u967d\u548c\u5730\u7403\u90fd\u5404\u4f54\u6709\u5f88\u5927\u7684\u7a7a\u9593\uff0c\u5982\u4f55\u6c7a\u5b9a\u592a\u967d\u8207\u5730\u7403\u7684\u8ddd\u96e2 R\uff1f\u592a\u967d\u548c\u5730\u7403\u96d6\u7136\u5f88\u5927\uff0c\u53ef\u662f\u548c R \u6bd4\u8d77\u4f86\uff0c\u537b\u662f\u5fae\u4e0d\u8db3\u9053\u3002\u56e0\u6b64\uff0c\u725b\u9813\u628a\u592a\u967d\u548c\u5730\u7403\u770b\u6210\u5169\u500b\u8cea\u9ede\uff0c\u5728\u592a\u967d\u88e1\u9762\u53d6\u4e00\u9ede\uff08<strong>S\u00a0<\/strong>\u9ede\uff09\uff0c\u9019\u5c31\u662f\u592a\u967d\u7684\u4f4d\u7f6e\uff0c\u5b83\u7684\u7e3d\u8cea\u91cf M\u88ab\u58d3\u7e2e\u5728\u00a0<strong>S\u00a0<\/strong>\u9ede\uff0c\u5728\u5730\u7403\u88e1\u9762\u53d6\u4e00\u9ede\uff08<strong>E\u00a0<\/strong>\u9ede\uff09\uff0c\u9019\u5c31\u662f\u5730\u7403\u7684\u4f4d\u7f6e\uff0c\u5b83\u7684\u7e3d\u8cea\u91cf m \u88ab\u58d3\u7e2e\u5728\u00a0<strong>E\u00a0<\/strong>\u9ede\u3002<strong>S\u00a0<\/strong>\u9ede\u548c\u00a0<strong>E\u00a0<\/strong>\u9ede\u7684\u8ddd\u96e2\u662f R\u3002\u6211\u5011\u53ef\u4ee5\u505a\u4e00\u500b\u60f3\u50cf\uff0c\u7528\u5f88\u591a\u5047\u60f3\u7684\u5e73\u9762\u628a\u592a\u967d\u5206\u6210\u5f88\u591a\u584a\uff1aA\u3001B\u3001C\u3001D\u2026\u7b49\u7b49\uff0c\u6bcf\u4e00\u584a\u5c0d\u5730\u7403\u90fd\u6709\u5f15\u529b\uff0c\u662f\u7d44\u6210\u592a\u967d\u7684\u7e3d\u5f15\u529b\u7684\u4e00\u500b\u5206\u529b\u3002\u7528\u725b\u9813\u7684\u300c\u8cea\u9ede\u6a21\u578b\u300d\u4f86\u8a08\u7b97\u6bcf\u4e00\u584a\u7684\u5206\u529b\uff0c\u6211\u5011\u5f97\u5148\u628a\u9019\u4e00\u584a\u7684\u8cea\u91cf\u58d3\u7e2e\u6210\u4e00\u9ede\uff0c\u7136\u5f8c\u628a\u5b83\u653e\u5728\u00a0<strong>S\u00a0<\/strong>\u9ede\u4e0a\u3002\u5982\u679c\u539f\u4f86\u7684 A \u584a\u7522\u751f\u7684\u5206\u529b\uff0c\u548c\u539f\u4f86\u7684 B \u584a\u7522\u751f\u7684\u5206\u529b\uff0c\u4e4b\u9593\u6709\u4efb\u4f55\u95dc\u806f\uff0c\u7576\u5b83\u5011\u500b\u5225\u7684\u8cea\u91cf\u88ab\u58d3\u7e2e\u6210\u4e00\u9ede\uff0c\u79fb\u653e\u5728\u00a0<strong>S\u00a0<\/strong>\u9ede\u4e0a\u4e4b\u5f8c\uff0cA\u584a\u548cB\u584a\u7522\u751f\u7684\u9019\u5169\u9805\u5206\u529b\uff0c\u4e4b\u9593\u5c31\u4e0d\u6703\u518d\u6709\u4efb\u4f55\u95dc\u806f\u4e86\u3002\u628a\u9019\u4e9b\u5206\u9805\u5f15\u529b\u52a0\u5728\u4e00\u8d77\uff0c\u5c31\u662f\u592a\u967d\u5c0d\u5730\u7403\u7684\u7e3d\u5f15\u529b\u3002\u56e0\u6b64\uff0c\u6211\u76f8\u4fe1\u4ee5\u4e0b\u9019\u500b\u5408\u7406\u7684\u7d50\u8ad6\u3002\u725b\u9813\u7528\u300c\u8cea\u9ede\u6a21\u578b\u300d\uff0c\u77e5\u9053\u5728\u4efb\u4f55\u5169\u500b\u8cea\u9ede\u4e4b\u9593\u90fd\u5b58\u5728\u8457\u300c\u5f15\u529b\u300d\u3002\u592a\u967d\u662f\u7531\u7121\u6578\u591a\u7684\u8cea\u9ede\u6240\u7d44\u6210\u7684\uff0c\u6bcf\u4e00\u500b\u8cea\u9ede\u5c0d\u5730\u7403\u90fd\u6709\u5f15\u529b\uff0c\u628a\u9019\u4e9b\u5f15\u529b\u52a0\u5728\u4e00\u8d77\uff0c\u5c31\u662f\u592a\u967d\u5c0d\u5730\u7403\u7684\u7e3d\u5f15\u529b\uff0c\u56e0\u6b64\uff0c\u7e3d\u5f15\u529b\u7684\u5927\u5c0f\u548c\u8cea\u91cf\u7684\u95dc\u4fc2\u662f\u300c\u7dda\u6027\u7684\u300d\u3002\u5148\u77e5\u5148\u89ba\u7684\u725b\u9813\uff0c\u80fd\u6d1e\u6089\u771f\u7406\u771f\u50cf\uff0c\u5f97\u5230\u4e86\u6b63\u78ba\u7684\u6578\u5b78\u8868\u9054\u5f0f F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\u3002\u904e\u4e86\u5e7e\u5e74\u4e4b\u5f8c\uff0c\u725b\u9813\u767c\u660e\u4e86\u300c\u5fae\u7a4d\u5206\u300d\uff0c\u518d\u7528\u300c\u8cea\u9ede\u6a21\u578b\u300d\u4f86\u7cbe\u78ba\u7684\u8a08\u7b97\u7e3d\u5f15\u529b\u6642\uff0c\u5c31\u4e0d\u9700\u8981\u628a\u4f4d\u65bc\u592a\u967d\u4e2d\u4efb\u4f55\u4e00\u9ede\u7684\u8cea\u91cf\u79fb\u52d5\u5230\u00a0<strong>S\u00a0<\/strong>\u9ede\u4e86\uff01<\/p>\n<p>\u5f8c\u77e5\u5f8c\u89ba\u7684\u6211\u9084\u662f\u60f3\u66f4\u6df1\u5165\u7684\u77e5\u9053 F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2\u00a0<\/sup>\u662f\u5982\u4f55\u88ab\u63a8\u5c0e\u51fa\u4f86\u7684\u3002\u6211\u7684\u5f1f\u5f1f\u8d99\u69ae\u5b89\uff08\u53f0\u5927\u7269\u7406\u7cfb1964\u5e74\u7562\u696d\uff09\u63d0\u9192\u6211\u5169\u500b\u91cd\u9ede\uff0c\u7b2c\u4e00\u500b\u91cd\u9ede\u662f\uff0c\u5982\u679c\u592a\u967d\u7684\u8cea\u91cf\u662f\u96f6 M=0\uff0c\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\u5c31\u6d88\u5931\u4e86 F<sub>M<\/sub>(m)=0\u3002\u9019\u500b\u689d\u4ef6\uff0c\u7d66\u4e86\u6211\u4e00\u500b\u91cd\u8981\u7684\u555f\u767c\uff0c\u53ef\u4ee5\u7528\u5728\u725b\u9813\u6642\u4ee3\u5c31\u5df2\u7d93\u6709\u7684\u201c\u7dda\u6027\u4ee3\u6578\u5b78\u201d\uff0c\u89e3\u201c\u591a\u5143\u4e00\u6b21\u806f\u7acb\u65b9\u7a0b\u5f0f\u201d\uff0c\u63a8\u5c0e\u51fa\u300c\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u300d\u7684\u5b8c\u6574\u6578\u5b78\u5f0f\u3002\u6211\u61c9\u8a72\u5148\u89e3\u8aaa\u4e00\u4ef6\u4e8b\u3002\u300c\u7dda\u6027\u4ee3\u6578\u300d\u7531\u4f86\u5df2\u65e9\uff0c\u300c\u96de\u5154\u540c\u7c60\u300d\u5c31\u662f\u53e4\u4ee3\u7684\u4e00\u500b\u7dda\u6027\u4ee3\u6578\u7684\u300c\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u5f0f\u300d\u7684\u6578\u5b78\u984c\u76ee\u3002\u73fe\u4ee3\u610f\u7fa9\u7684\u7dda\u6027\u4ee3\u6578\u51fa\u73fe\u65bc\u725b\u9813\u6642\u4ee3\u7684\u5341\u4e03\u4e16\u7eaa\u3002\u7d93\u904e\u4e00\u767e\u591a\u5e74\u7684\u6f14\u9032\uff0c\u76f4\u5230\u5341\u4e5d\u4e16\u7eaa\u6642\uff0c\u624d\u5b8c\u6210\u4e86\u5f9e\u4e09\u7dad\u7dda\u6027\u7a7a\u9593\u5230\u00a0<strong>n<\/strong> \u7dad\u7dda\u6027\u7a7a\u9593\u7684\u904e\u6e21\u3002\u540c\u6642\uff0c\u7531\u65bc\u884c\u5217\u5f0f\u548c\u77e9\u9663\u7684\u7522\u751f\uff0c\u70ba\u8655\u7406\u7dda\u6027\u554f\u984c\u63d0\u4f9b\u4e86\u6709\u529b\u7684\u5de5\u5177\u3002\u65bc\u662f\u9032\u4e00\u6b65\u7684\u767c\u5c55\u51fa\u51fd\u6578\u7406\u8ad6\uff0c \u548c\u6211\u5011\u73fe\u5728\u7684\u8a0e\u8ad6\u6709\u95dc\u7684\uff0c f(x+y)=f(x)+f(y) \u9019\u4e00\u985e\u7684\u300c\u7dda\u6027\u51fd\u6578\u300d\uff0c\u5b83\u7684\u300c\u89e3\u300d\u90fd\u6709\u90a3\u5e7e\u985e\uff0c\u4ee5\u53ca\u4ed6\u5011\u5206\u5225\u90fd\u6709\u4ec0\u9ebc\u6578\u5b78\u6027\u8cea\uff0c\u4e5f\u662f\u4e00\u6642\u7684\u91cd\u8981\u7814\u7a76\u4e3b\u984c\u3002\u5982\u679c\u6211\u5011\u7528\u73fe\u5728\u77e5\u9053\u7684\u300c\u7dda\u6027\u51fd\u6578\u300d\u7684\u7406\u8ad6\uff0c\u7acb\u523b\u5c31\u5f97\u5230 F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\u3002\u4e0d\u904e\uff0c\u9019\u4e9b\u300c\u6211\u5011\u73fe\u5728\u77e5\u9053\u300d\u7684\u6578\u5b78\u7d50\u8ad6\uff0c\u90fd\u662f\u725b\u9813\u8eab\u5f8c\u767c\u751f\u7684\u4e8b\u3002<\/p>\n<p>\u6211\u5011\u5c31\u7528\u725b\u9813\u6642\u5df2\u6709\u7684\u6578\u5b78\u77e5\u8b58\uff0c\u5f9e F<sub>M<\/sub>(m) \u221e C(M)m\/R<sup>2<\/sup>\u00a0 \u958b\u59cb\u4f86\u8003\u616e\u554f\u984c\u3002\u70ba\u4e86\u65b9\u4fbf\u8868\u8ff0\uff0c\u6211\u628a\u6bd4\u4f8b\u5e38\u6578\u5305\u542b\u5728 C(M) \u4e2d\uff0c\u5beb\u6210 F<sub>M<\/sub>(m)=C(M)m\/R<sup>2<\/sup>\u3002\u56e0\u70ba\u7576 M=0 \u6642\uff0cC(0)=0\uff0c\u6211\u5011\u53ef\u4ee5\u7528\u4e00\u500b\u300c\u4e00\u822c\u89e3\u300d\u7684\u5f62\u5f0f\u628a C(M) \u8868\u9054\u6210<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-30904\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/05\/01.png\" alt=\"\" width=\"500\" height=\"44\" \/><\/p>\n<p>\u6b64\u8655\u7684 X<sub>2<\/sub>\uff0cX<sub>3<\/sub>\uff0cX<sub>4<\/sub>\uff0c\uff0e\uff0e\uff0e\u7686\u70ba\u5f85\u5b9a\u7684\u4fc2\u6578\uff0ca2\uff0ca3\uff0ca4\uff0c\uff0e\uff0e\uff0e\u53ef\u4ee5\u6709\u4e0d\u7b49\u65bc 1 \u7684\u4efb\u4f55\u6b63\u6578\u503c\u3002\u73fe\u5728\u6211\u5011\u60f3\u50cf\uff0c\u592a\u967d\u88ab\u5206\u6210\u5f88\u591a\u584a\uff0c\u6bcf\u4e00\u584a\u5c0d\u5730\u7403\u90fd\u6709\u5f15\u529b\uff0c\u628a\u9019\u4e9b\u5f15\u529b\u52a0\u5728\u4e00\u8d77\uff0c\u5c31\u662f\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\u3002\u8b93\u6211\u5011\u8003\u616e\u7b2c\u4e00\u7a2e\u5206\u6cd5\uff0c\u628a\u592a\u967d\u5206\u6210\u5169\u584a\uff0c\u4e00\u584a\u7684\u8cea\u91cf\u662f M\/3\uff0c\u53e6\u4e00\u584a\u7684\u8cea\u91cf\u662f 2M\/3\u3002\u5b83\u5011\u5404\u5225\u5c0d\u5730\u7403\u7684\u5f15\u529b\u662f F<sub>M\/3<\/sub>(m)=C(M\/3)m\/R<sup>2<\/sup>\uff0c\u5176\u4e2d<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-30905\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/05\/02.png\" alt=\"\" width=\"633\" height=\"244\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u5982\u679c\u628a X<sub>2<\/sub>\uff0cX<sub>3<\/sub>\uff0cX<sub>4<\/sub>\uff0c\uff0e\uff0e\uff0e\u770b\u6210\u5f85\u89e3\u7684\u672a\u77e5\u5143\uff0c\u4ee5\u4e0a\u7684\u300c\u591a\u5143\u4e00\u6b21\u65b9\u7a0b\u5f0f\u300d\u53ef\u4ee5\u5beb\u6210<\/p>\n<p><img decoding=\"async\" class=\"alignleft wp-image-30917 size-full\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/05\/03-1.png\" alt=\"\" width=\"761\" height=\"112\" \/><\/p>\n<p>\u5047\u60f3\u628a\u592a\u967d\u5206\u6210\u5f88\u591a\u584a\uff0c\u6709\u5e7e\u4e4e\u7121\u7aae\u591a\u7a2e\u5206\u6cd5\u3002\u76f8\u5c0d\u65bc\u6bcf\u4e00\u7a2e\u5206\u6cd5\uff0c\u5c31\u6709\u4e00\u500b\u985e\u4f3c\u7684\u65b9\u7a0b\u5f0f\uff0c\u53ea\u662f\u5176\u4e2d\u7684\u4fc2\u6578\u4e0d\u540c\u3002\u6211\u5011\u628a\u7b2c\u201ci\u201d\u7a2e\u5206\u6cd5\u7684\u76f8\u5c0d\u7684\u90a3\u4e00\u7d44\u4fc2\u6578\u8868\u9054\u70ba\u00a0 (C<sub>i,2<\/sub>,C<sub>i,3<\/sub>,C<sub>i,4<\/sub>\uff0e\uff0e\uff0e)\u3002\u65bc\u662f\u6211\u5011\u5f97\u5230\u4e00\u7d44\u300c\u591a\u5143\u4e00\u6b21\u806f\u7acb\u65b9\u7a0b\u5f0f\u300d<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-30907\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/05\/04.png\" alt=\"\" width=\"462\" height=\"167\" \/><\/p>\n<p>\u5728\u9019\u500b\u300c\u591a\u5143\u806f\u7acb\u65b9\u7a0b\u5f0f\u300d\u4e2d\uff0c\u6709\u5e7e\u4e4e\u7121\u7aae\u591a\u5143\uff0c\u4e5f\u6709\u5e7e\u4e4e\u7121\u7aae\u591a\u500b\u65b9\u7a0b\u5f0f\u3002\u9664\u4e86\u6240\u6709\u7684 X<sub>2<\/sub>=X<sub>3<\/sub>=X<sub>4<\/sub>=\uff0e\uff0e\uff0e=0 \u9019\u500b\u89e3\u4e4b\u5916\uff0c\u5f88\u96e3\u60f3\u50cf\u5b58\u5728\u8457 X<sub>i<\/sub>\u00a0\u22600 \u00a0\u7684\u89e3\u3002\u5373\u4f7f\u5b58\u5728\u8457 X<sub>i<\/sub>\u00a0\u22600\u7684\u89e3\uff0c\u9019\u4e00\u7d44\u7b54\u6848\u4e5f\u53ea\u662f\u76f8\u5c0d\u65bc\u592a\u967d\u7684\u8cea\u91cf M\u3002\u5982\u679c\u628a M \u63db\u6210\u5730\u7403\u7684\u8cea\u91cf m\uff0c\u4f86\u8a08\u7b97\u5730\u7403\u5c0d\u6708\u7403\u7684\u5438\u5f15\u529b\uff0c\u56e0\u70ba\u6240\u6709\u7684\u4fc2\u6578 C<sub>i,n<\/sub> \u7684\u6578\u503c\u90fd\u8b8a\u4e86\uff0c\u6211\u5011\u5f97\u5230\u7684\u662f\u53e6\u5916\u4e00\u7d44\u00a0 X<sub>i<\/sub>\u00a0\u22600 \u7684\u89e3\u3002\u9019\u7a2e\u300c\u9055\u53cd\u81ea\u7136\u73fe\u8c61\u300d\u7684\u6578\u5b78\u7b54\u6848\uff0c\u662f\u7269\u7406\u754c\u4e0d\u80fd\u63a5\u53d7\u7684\u300c\u975e\u7269\u7406\u7b54\u6848\u300d\u3002<\/p>\n<p>\u6211\u5011\u80fd\u63a5\u53d7\u7684\uff0c\u5408\u4e4e\u81ea\u7136\u73fe\u8c61\u7684\u300c\u7269\u7406\u89e3\u300d\u662f X<sub>2<\/sub>=X<sub>3<\/sub>=X<sub>4<\/sub>=\uff0e\uff0e\uff0e=0\u3002\u6211\u5011\u5f9e\u201c\u5f0f-(1)\u201d\u4e2d\u5c31\u5f97\u5230 C(M)=CM\uff0c\u9032\u800c\u5f97\u5230\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\u662f F<sub>M<\/sub>(m)=CMm\/R<sup>2<\/sup>\u3002\u6309\u7167\u540c\u6a23\u7684\u9053\u7406\uff0c\u5730\u7403\u5c0d\u592a\u967d\u7684\u5f15\u529b\u4e5f\u662f F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\u3002\u9019\u5c31\u662f\u725b\u9813\u7684\u842c\u6709\u5f15\u529b\u5b9a\u5f8b<\/p>\n<p style=\"text-align: center;\">F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup><\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5169\u500b\u7269\u9ad4\u4e4b\u9593\u7684\u300c\u63a5\u89f8\u300d\u76f8\u4e92\u4f5c\u7528<\/strong><\/span><\/p>\n<p>1666\u5e74\u725b\u9813\u767c\u73fe\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\uff0c\u4e8c\u5341\u4e00\u5e74\u5f8c\uff0c1687\u5e74\u725b\u9813\u51fa\u7248\u529b\u4ed6\u7684\u4e09\u500b\u904b\u52d5\u5b9a\u5f8b\u3002\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\uff0cf(t)=d[m(t)v(t)]\/dt\uff0c\u628a\u201c\u529b\u201d f(t) \u5b9a\u7fa9\u70ba\u52d5\u91cf [m(t)v(t)] \u96a8\u6642\u9593 t \u7684\u6539\u8b8a\u7387\u3002\u5982\u679c\u6c92\u6709\u529b\u52a0\u5728\u4e00\u500b\u7269\u9ad4\u4e0a\uff0cf(t)=0\uff0c\u5b83\u7684\u52d5\u91cf\u5c31\u662f\u4e00\u500b\u4e0d\u96a8\u6642\u9593\u6539\u8b8a\u7684\u5b9a\u503c\u3002\u73fe\u5728\u6211\u5011\u8003\u616e\u5169\u500b\u7269\u9ad4\u4e92\u76f8\u78b0\u649e\u3002\u7b2c\u4e00\u500b\u7269\u9ad4\u7684\u52d5\u91cf\u5728\u78b0\u649e\u524d\u662f P<sub>1<\/sub>\uff0c\u5728\u78b0\u649e\u5f8c\u662f P<sub>2<\/sub>\u3002\u7b2c\u4e8c\u500b\u7269\u9ad4\u7684\u52d5\u91cf\u5728\u78b0\u649e\u524d\u662f Q<sub>1<\/sub>\uff0c\u5728\u78b0\u649e\u5f8c\u662f Q<sub>2<\/sub>\u3002\u56e0\u70ba\u6c92\u6709\u300c\u5916\u529b\u300d\u52a0\u5728\u9019\u5169\u500b\u7269\u9ad4\u4e0a\uff0c\u5b83\u5011\u7684\u7e3d\u52d5\u91cf\u5c31\u4e0d\u6703\u56e0\u70ba\u4e92\u78b0\u800c\u6539\u8b8a\uff0c\u6240\u4ee5 P<sub>1<\/sub>+Q<sub>1<\/sub>=P<sub>2<\/sub>+Q<sub>2<\/sub>\uff0c\u6216\u8005\u5beb\u6210 P<sub>2<\/sub> -P<sub>1<\/sub>=-(Q<sub>2<\/sub>-Q<sub>1<\/sub>)\u3002\u6211\u5011\u7528 <strong>T <\/strong>\u8868\u793a\u4e92\u76f8\u78b0\u649e\u6240\u7d93\u6b77\u7684\u6642\u9593\uff0c\u7528\u725b\u9813\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\uff0c\u6211\u5011\u5c31\u5f97\u5230\uff0c\u7b2c\u4e8c\u500b\u7269\u9ad4\u52a0\u5728\u7b2c\u4e00\u500b\u7269\u9ad4\u4e0a\u7684\u529b\u662f F<sub>1<\/sub>=(P<sub>2<\/sub>-P<sub>1<\/sub>)\/T\uff0c\u7b2c\u4e00\u500b\u7269\u9ad4\u52a0\u5728\u7b2c\u4e8c\u500b\u7269\u9ad4\u4e0a\u7684\u529b\u662f F<sub>2<\/sub>=(Q<sub>2<\/sub>-Q<sub>1<\/sub>)\/T\uff0c\u4ea6\u5373 F<sub>2<\/sub>=-F<sub>1<\/sub>\u3002\u6240\u4ee5\uff0c\u5169\u500b\u7269\u9ad4\u4f5c\u300c\u63a5\u89f8\u529b\u300d\u7684\u4e92\u76f8\u4f5c\u7528\u6642\uff0c\u4f5c\u7528\u529b\u548c\u53cd\u4f5c\u7528\u529b\u7684\u5927\u5c0f\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u53cd\u3002<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u725b\u9813\u7b2c\u4e09\u904b\u52d5\u5b9a\u5f8b<\/strong><\/span><\/p>\n<p>\u57281666\u5e74\u725b\u9813\u767c\u73fe\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u6642\uff0c\u300c\u529b\u300d\u9084\u53ea\u662f\u4e00\u500b\u89c0\u5ff5\uff0c\u5230\u725b\u9813\u5f97\u5230\u7b2c\u4e8c\u904b\u52d5\u5b9a\u5f8b\u6642\uff0c\u624d\u78ba\u5b9a\u4e86\u300c\u529b\u662f\u4e00\u500b\u80fd\u6e2c\u51fa\u7684\u7269\u7406\u91cf\u300d\u3002\u6211\u5f1f\u5f1f\u8d99\u69ae\u5b89\u63d0\u9192\u6211\u7684\u7b2c\u4e8c\u500b\u91cd\u9ede\u662f\uff0c\u6839\u64da\u00a0 F<sub>M<\/sub>(m)=F<sub>m<\/sub>(M)=CMm\/R<sup>2<\/sup>\u00a0 \u9019\u500b\u6578\u5b78\u5f0f\uff0c\u6e2c\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\uff0c\u548c\u6e2c\u5730\u7403\u5c0d\u592a\u967d\u7684\u5f15\u529b\uff0c\u6703\u5f97\u5230\u540c\u4e00\u500b\u6578\u503c\u3002\u56e0\u6b64\uff0c\u592a\u967d\u5c0d\u5730\u7403\u7684\u5f15\u529b\uff0c\u548c\u5730\u7403\u5c0d\u592a\u967d\u7684\u5f15\u529b\uff0c\u4e26\u4e0d\u662f\u5169\u500b\u7368\u7acb\u7684\u529b\uff0c\u800c\u662f\u4e00\u500b\u529b\u3002\u6240\u4ee5\u5728\u725b\u9813\u63a8\u5c0e\u51fa\uff0c\u300c\u5169\u500b\u7269\u9ad4\u4f5c\u63a5\u89f8\u529b\u7684\u4e92\u76f8\u4f5c\u7528\u6642\uff0c\u4f5c\u7528\u529b\u548c\u53cd\u4f5c\u7528\u529b\u7684\u5927\u5c0f\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u53cd\u300d\u4e4b\u5f8c\uff0c\u4e00\u5b9a\u662f\u5f88\u5feb\u7684\u5c31\u4e86\u89e3\u5230\uff0c\u4ee5\u4e0a\u7684\u6578\u5b78\u8868\u9054\u5f0f\uff0c\u6240\u4ee3\u8868\u7684\u7269\u7406\u4f5c\u7528\uff0c\u662f\u4e00\u500b\u300c\u4e92\u76f8\u4f5c\u7528\u529b\u300d\uff0c\u662f\u592a\u967d\u548c\u5730\u7403\u5169\u500b\u975e\u63a5\u89f8\u7269\u9ad4\u4e4b\u9593\u7684\uff0c\u5927\u5c0f\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u53cd\u7684\u300c\u4f5c\u7528\u53cd\u4f5c\u7528\u529b\u300d\u3002\u5230\u6b64\u6642\uff0c\u725b\u9813\u5c31\u5b8c\u6574\u7684\u5efa\u7acb\u4e86\u4ed6\u7684\u7b2c\u4e09\u904b\u52d5\u5b9a\u5f8b\u3002<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5f8c\u8a18\uff1a\u5929\u6587\u529b\u5b78\u65b0\u7d00\u5143<\/strong><\/span><\/p>\n<p>\u592a\u967d\u548c\u5730\u7403\u4e4b\u9593\u7684\u76f8\u4e92\u300c\u4f5c\u7528\u53cd\u4f5c\u7528\u529b\u300d\uff0c\u4e0d\u6703\u6539\u8b8a\u300c\u592a\u967d\u548c\u5730\u7403\u7684\u7e3d\u52d5\u91cf\u300d\u3002\u5982\u679c\u5728\u300c\u55ae\u4f4d\u6642\u9593\u300d\u5167\uff0c\u5730\u7403\u7684\u901f\u5ea6\u6539\u8b8a\u662fU<sub>E<\/sub>\uff0c\u592a\u967d\u7684\u901f\u5ea6\u6539\u8b8a\u5c31\u662f U<sub>s<\/sub>=-(m\/M) U<sub>E<\/sub>\uff0cU<sub>s<\/sub> \u7684\u503c\u6bd4 U<sub>E<\/sub> 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