{"id":109908,"date":"2025-08-10T01:04:10","date_gmt":"2025-08-10T05:04:10","guid":{"rendered":"https:\/\/minzhuzhongguo.org\/?p=109908"},"modified":"2025-08-09T18:50:40","modified_gmt":"2025-08-09T22:50:40","slug":"%e6%b1%9f%e6%a3%8b%e7%94%9f%ef%bc%9a%e6%97%b6%e9%97%b4%e5%9d%90%e6%a0%87%e5%8f%8d%e5%b0%84%e5%8f%98%e6%8d%a2%ef%bc%9a%e6%97%b6%e9%97%b4%e6%ad%a3%e5%8f%8d%e6%b5%81%e5%90%91%e4%b9%8b%e5%8f%98%e6%8d%a2","status":"publish","type":"post","link":"https:\/\/minzhuzhongguo.org\/?p=109908","title":{"rendered":"\u6c5f\u68cb\u751f\uff1a\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362\uff1a\u65f6\u95f4\u6b63\u53cd\u6d41\u5411\u4e4b\u53d8\u6362\uff0c\u8fd8\u662f\u987a\u5012\u8ba1\u65f6\u65b9\u5f0f\u4e4b\u53d8\u6362\uff1f"},"content":{"rendered":"

\u5728\u300a\u65f6\u95f4\u95f4\u9694\u5e94\u8be5\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c\u6765\u8868\u5f81\u300b[1]\u4e00\u6587\u4e2d\uff0c\u6211\u5bf9\u987a\u8ba1\u65f6\u4e0e\u5012\u8ba1\u65f6\u4e24\u79cd\u65b9\u5f0f\u4f5c\u4e86\u521d\u6b65\u8003\u5bdf\u3002\u6211\u7ed9\u51fa\u7684\u7ed3\u8bba\u662f\uff1a\u5728\u987a\u8ba1\u65f6\u4e0b\uff0c\u65f6\u95f4\u95f4\u9694\u53ef\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\uff08\u4e5f\u79f0\u65f6\u95f4\u5750\u6807\u589e\u91cf\uff09\u0394t \u6765\u8868\u5f81\uff1b\u56e0\u4e3a t \u662f\u9012\u589e\u7684\uff0c\u603b\u6709\u0394t > 0\u3002\u4f46\u5728\u5012\u8ba1\u65f6\u4e0b\uff0c\u65f6\u95f4\u95f4\u9694\u5c31\u4e0d\u80fd\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u0394\uf074\u6765\u8868\u5f81\uff1b\u56e0\u4e3a\uf074\u662f\u9012\u51cf\u7684\uff0c\u603b\u6709\u0394\uf074<0\uff1b\u8fd9\u65f6\uff0c\u65f6\u95f4\u95f4\u9694\u5c31\u987b\u7528\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u7684\u7edd\u5bf9\u503c\u6765\u8868\u5f81\uff0c<\/p>\n

\u5373\u7528|\u0394\uf074 |\u6765\u8868\u5f81\u3002<\/p>\n

\u73b0\u5728\uff0c\u6211\u4eec\u6765\u8003\u5bdf\u987a\u5012\u8ba1\u65f6\u65b9\u5f0f\u4e4b\u95f4\u7684\u5750\u6807\u53d8\u6362\u5173\u7cfb\u3002<\/p>\n

\u8bbe\u4e24\u4f4d\u89c2\u5bdf\u8005\u5bf9\u540c\u4e00\u4e8b\u4ef6\u7684\u8fdb\u7a0b\uff0c\u5982\u8fd0\u8f7d\u706b\u7bad\u53d1\u5c04\u524d\u6700\u540e10\u79d2\u4e4b\u8fdb\u7a0b\uff0c\u5404\u81ea\u8fdb\u884c\u89c2\u5bdf\u3002\u4e00\u4f4d\u91c7\u7528\u987a\u8ba1\u65f6\uff1b\u53e6\u4e00\u4f4d\u91c7\u7528\u5012\u8ba1\u65f6\uff0c\u5012\u8ba1\u65f6\u65f6\u6bb5\u4e3a10\u79d2\u300210\u79d2\u4e4b\u540e\uff0c\u706b\u7bad\u70b9\u706b\u3002\u5bf9\u8fdb\u7a0b\u7684\u6bcf\u4e00\u65f6\u523b\uff0c\u4e24\u4f4d\u89c2\u5bdf\u8005\u5404\u81ea\u6d4b\u5f97\u7684\u65f6\u95f4\u5750\u6807\u5982\u4e0b\uff1a<\/p>\n

\u987a\u8ba1\u65f6\u5750\u6807t\uff1a 0\uff0c 1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c7\uff0c8\uff0c9\uff0c10\uff1b
\n\u5012\u8ba1\u65f6\u5750\u6807\uf074\uff1a10, 9\uff0c8\uff0c7\uff0c6\uff0c5\uff0c4\uff0c3\uff0c2\uff0c1\uff0c0.<\/p>\n

\u4e0a\u8ff0\u65f6\u95f4\u5750\u6807t\u4e0e\uf074\u7684\u6d4b\u91cf\u7ed3\u679c\u4e4b\u95f4\uff0c\u5b58\u5728\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u4e0d\u96be\u770b\u51fa\uff0c\u65f6\u95f4\u5750\u6807t\u4e0e\uf074 \u4e4b\u95f4\u6709\u5982\u4e0b\u53d8\u6362\u5173\u7cfb\uff1a
\n\uf074=-t+10. (1)
\n\u4e00\u822c\u5730\uff0c\u53ef\u8bbe\u5012\u8ba1\u65f6\u65f6\u6bb5\u4e3aD\u79d2\uff0c\u5219\u53d8\u6362\u5173\u7cfb\u4e3a\uff1a
\n\uf074=-t+D (2)
\n\u73b0\u5728\uff0c\u6211\u4eec\u5bf9\uf074\u4f5c\u4e00\u4e2a\u5e73\u79fb\u53d8\u6362
\nt’=\uf0a2-D (3)
\n\u5219\u53ef\u7acb\u5f97\uff1a
\nt’=-t (4)<\/p>\n

\u800c\u5f0f(4)\uff0c\u6b63\u662f\u4eba\u4eec\u65e9\u5df2\u719f\u77e5\u7684\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362\uff1a<\/p>\n

t->\u00a0 t’=-t\u00a0 (5)<\/p>\n

\u7531\u6b64\u53ef\u77e5\uff0c\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362\u4e4b\u771f\u4e49\uff0c\u4e43\u662f\u987a\u8ba1\u65f6\u4e0e\u5012\u8ba1\u65f6\u4e24\u79cd\u8ba1\u65f6\u65b9\u5f0f\u4e4b\u53d8\u6362\uff0c\u53ef\u7b80\u79f0\u4e3a\u8ba1\u65f6\u65b9\u5f0f\u53d8\u6362\u3002t\u4e3a\u987a\u8ba1\u65f6\u5750\u6807\uff0c\u2014t\u4e3a\u5012\u8ba1\u65f6\u5750\u6807\uff1bt\u548c\u2014t\uff0c\u8868\u5f81\u76f8\u540c\u7684\u65f6\u95f4\u65b9\u5411\u3002<\/p>\n

\u53ef\u53f9\u7684\u662f\uff0c100\u591a\u5e74\u6765\uff0c\u4eba\u4eec\u5374\u4e00\u76f4\u8bef\u628a\u677e\u679d\u6807\u85e4\u6761\uff0c\u8bef\u4ee5\u4e3a\uff1a\u65f6\u95f4\u5750\u6807t\u8868\u5f81\u65f6\u95f4\u7684\u6b63\u5411\u6d41\u52a8\uff0c\u800c\u65f6\u95f4\u5750\u6807\u2014t\u5219\u8868\u5f81\u65f6\u95f4\u7684\u53cd\u5411\u6d41\u52a8\uff1b\u56e0\u6b64\u65f6\u95f4\u5750\u6807\u7684\u53cd\u5c04\u53d8\u6362\uff08T\u53d8\u6362\uff09\uff0c\u5c31\u662f\u65f6\u95f4\u6b63\u53cd\u6d41\u5411\u4e4b\u95f4\u7684\u53d8\u6362\uff0c\u5373\u6240\u8c13\u65f6\u95f4\u53cd\u6f14\u3002\u4f8b\u5982\uff0c\u725b\u6d25\u5927\u5b66\u5f6d\u7f57\u65af\u6559\u6388\u5728\u300a\u7687\u5e1d\u65b0\u8111\u300b[2]\u4e00\u4e66\u4e2d\u8bf4\uff1a<\/p>\n

\u6240\u6709\u6210\u529f\u7684\u7269\u7406\u65b9\u7a0b\u90fd\u5728\u65f6\u95f4\u4e0a\u662f\u5bf9\u79f0\u7684\u3002\u5b83\u4eec\u5728\u65f6\u95f4\u7684\u4efb\u4f55\u65b9\u5411\u4e0a\u4f7f\u7528\u90fd\u663e\u5f97\u4e00\u6837\u3002\u5728\u7269\u7406\u5b66\u4e0a\uff0c\u5c06\u6765\u548c\u8fc7\u53bb\u4f3c\u4e4e\u662f\u5e73\u6743\u7684\u3002\u725b\u987f\u65b9\u7a0b\u3001\u54c8\u5bc6\u987f\u65b9\u7a0b\u3001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u548c\u7231\u56e0\u65af\u5766\u5f15\u529b\u573a\u65b9\u7a0b\u3001\u72c4\u62c9\u514b\u65b9\u7a0b\u548c\u859b\u5b9a\u8c14\u65b9\u7a0b\u2014\u2014\u5982\u679c\u6211\u4eec\u98a0\u5012\u65f6\u95f4\u65b9\u5411\uff08\u7528\u2014t\u6765\u53d6\u4ee3\u4ee3\u8868\u65f6\u95f4\u7684\u5750\u6807t\uff09\uff0c\u6240\u6709\u8fd9\u4e9b\u65b9\u7a0b\u5728\u5b9e\u8d28\u4e0a\u90fd\u4e0d\u53d8\u3002<\/p>\n

\u5728T\u53d8\u6362\u7684\u5b9e\u8d28\u5f97\u4ee5\u63ed\u793a\u4e4b\u540e\uff0c\u6211\u4eec\u8981\u5f15\u51fa\u4e00\u4e2a\u91cd\u8981\u7684\u7ed3\u8bba\uff1a\u7531\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362\u5373\u8ba1\u65f6\u65b9\u5f0f\u53d8\u6362t\u2192t’=\u2014t\u6240\u5f15\u53d1\u7684\u7269\u7406\u91cf\u53d8\u6362\u4e2d\uff0c\u53ea\u6709\u4fdd\u6301\u4e0d\u53d8\u7684\u5076\u53d8\u91cf\uff0c\u6ca1\u6709\u6539\u53d8\u7b26\u53f7\u7684\u5947\u53d8\u91cf\u3002<\/p>\n

\u5728\u6240\u8c13\u201c\u65f6\u95f4\u53cd\u6f14\u201d\u4e0b\uff0c\u4ee5\u65f6\u95f4\u7684\u4e00\u9636\u5bfc\u6570\u6765\u8868\u793a\u7684\u201c\u901f\u5ea6\u201d\u8fd9\u4e00\u7269\u7406\u91cf\uff0c\u662f\u5178\u578b\u7684\u5947\u53d8\u91cf\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u6765\u770b\u770b\uff0c\u5728\u5012\u8ba1\u65f6t’\u4e0b\uff0c\u8d28\u70b9\u7684\u901f\u5ea6\u8be5\u5982\u4f55\u6c42\u5f97\u3002\u4e3a\u7b80\u660e\u8d77\u89c1\uff0c\u6211\u4eec\u5206\u6790\u8d28\u70b9\u4ecex1\u8fd0\u52a8\u5230x2\u7684\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\uff0c\u6c42\u51fa\u5012\u8ba1\u65f6t’\u4e0b\uff0c\u8d28\u70b9\u5728\u8fd9\u4e00\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\u7684\u5e73\u5747\u901f\u5ea6\uff0c\u4ee5\u53ca\u4e0a\u8ff0\u8fc7\u7a0b\u5185\u67d0\u4e00\u65f6\u523b\u7684\u8d28\u70b9\u77ac\u65f6\u901f\u5ea6\u3002
\n\"\"
\n\u56fe\u8d28\u70b9\u76f4\u7ebf\u8fd0\u52a8\u793a\u610f\u56fe<\/p>\n

\u53c2\u7167\u6587\u732e[1]\uff0c\u6211\u4eec\u5bb9\u6613\u5199\u51fa\uff1a\u5728\u5012\u8ba1\u65f6t’\u4e0b\uff0c\u65f6\u95f4\u5750\u6807\u6539\u53d8\u91cf\u4e3a
\n\u0394t’=t’\u665a\u2014t’\u65e9<0, (6)<\/p>\n

\u800c\u65f6\u95f4\u95f4\u9694\u5219\u4e3a|\u0394t’|\uff08\u5bf9\u5e73\u5747\u901f\u5ea6\u800c\u8a00\uff09\u548c|dt’|\uff08\u5bf9\u77ac\u65f6\u901f\u5ea6\u800c\u8a00\uff09\uff1a<\/p>\n

|\u0394t’|=-\u0394t’=\u0394t;\u00a0 |dt’|=-dt’=dt (7)<\/p>\n

\u4e8e\u662f\uff0c\u5012\u8ba1\u65f6t’\u4e0b\u7684\u8d28\u70b9\u5e73\u5747\u901f\u5ea6\u4e3a\uff1a<\/p>\n

\"\"(8)
\n\u8d28\u70b9\u77ac\u65f6\u901f\u5ea6\u4e3a\uff1a
\n\"\"(9)
\n\u5f0f(8)\u548c\u5f0f(9)\u8868\u660e\uff0c\u5728t\u2192t’=\u2014t\u7684T\u53d8\u6362\u4e0b\uff0c\u901f\u5ea6\u8fd9\u4e00\u7269\u7406\u91cf\u4fdd\u6301\u4e0d\u53d8\uff0c\u5e76\u672a\u53cd\u5411\u3002\u56e0\u6b64\uff0c\u901f\u5ea6\u662f\u5076\u53d8\u91cf\uff0c\u4e0d\u662f\u5947\u53d8\u91cf\u3002
\n\u90a3\u4e48\uff0c\u73b0\u6709\u7406\u8bba\u4e2d\u7684\u201c\u901f\u5ea6\u53cd\u5411\u201d\u548c\u201c\u901f\u5ea6\u662f\u5947\u53d8\u91cf\u201d\u662f\u5982\u4f55\u5f97\u6765\u7684\u5462\uff1f\u90a3\u662f\u56e0\u4e3a\uff0c\u4eba\u4eec\u8bef\u8ba4\u4e3a\u5728t’\u7cfb\u4e0b\uff0c\u65f6\u95f4\u95f4\u9694\u4e3a\u0394t’\uff08\u5bf9\u5e73\u5747\u901f\u5ea6\u800c\u8a00\uff09\u548cdt’\uff08\u5bf9\u77ac\u65f6\u901f\u5ea6\u800c\u8a00\uff09\uff0c\u4ed6\u4eec\u6709\uff1a
\nAt’=-At; dt=-dt (10)
\n\u968f\u4e4b\uff0c\u8d28\u70b9\u5e73\u5747\u901f\u5ea6\u5c31\u4e3a\uff1a
\n\"\"(11)
\n\u8d28\u70b9\u77ac\u65f6\u901f\u5ea6\u5219\u4e3a\uff1a
\n\"\"(12)
\n\u4e8e\u662f\uff0c\u6839\u636e\u5f0f\uff0811\uff09\u548c\uff0812\uff09\uff0c\u4eba\u4eec\u5f97\u51fa\u4e86T\u53d8\u6362\u4e0b\u201c\u901f\u5ea6\u53cd\u5411\u201d\u548c\u201c\u901f\u5ea6\u662f\u5947\u53d8\u91cf\u201d\u7684\u9519\u8bef\u7ed3\u8bba\u3002<\/p>\n

\u901f\u5ea6\u662f\u65f6\u95f4\u7684\u4e00\u9636\u5bfc\u6570\uff1b\u5728t\u2192t’=\u2014t\u7684T\u53d8\u6362\u4e0b\u901f\u5ea6\u4fdd\u6301\u4e0d\u53d8\u8fd9\u4e00\u4e8b\u5b9e\uff0c\u5b8c\u5168\u53ef\u4ee5\u63a8\u5e7f\u5230\u4e00\u822c\u60c5\u5f62\uff1a\u5373\u4efb\u4f55\u4ee5\u65f6\u95f4\u7684\u4e00\u9636\u5bfc\u6570\u6765\u8868\u793a\u7684\u7269\u7406\u91cf\uff0c\u5728\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362\u4e0b\u5747\u4fdd\u6301\u4e0d\u53d8\u3002\u56e0\u6b64\uff0c\u5728\u65f6\u95f4\u5750\u6807\u53cd\u5c04\u53d8\u6362t\u2192t’=\u2014t\u4e0b\uff0c\u53ea\u6709\u5076\u53d8\u91cf\uff0c\u6ca1\u6709\u5947\u53d8\u91cf\u3002<\/p>\n

\u770b\u6765\uff0c\u5df2\u6709100\u591a\u5e74\u5386\u53f2\u7684\u65f6\u95f4\u53cd\u6f14\u7269\u7406\u5b66\uff0c\u5c06\u4f1a\u88ab\u98a0\u8986\u6027\u5730\u6539\u5199\u4e3a\u8ba1\u65f6\u65b9\u5f0f\u53d8\u6362\u7269\u7406\u5b66\u3002<\/p>\n

2025\u5e743\u670830\u65e5\u521d\u7a3f
\n2025\u5e745\u670821\u65e5\u4fee\u6539<\/p>\n

\u53c2\u8003\u6587\u732e\uff1a<\/p>\n

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