{"id":21972,"date":"2025-10-08T21:01:06","date_gmt":"2025-10-08T13:01:06","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21972"},"modified":"2025-10-09T00:13:19","modified_gmt":"2025-10-08T16:13:19","slug":"%e4%b8%80%e7%a7%8d%e7%ab%8b%e5%bc%8f%e5%b9%b3%e8%a1%a1%e6%9c%ba%e6%b5%8b%e9%87%8f%e4%b8%8d%e5%b9%b3%e8%a1%a1%e9%87%8f%e7%9a%84%e5%8e%9f%e7%90%86","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21972","title":{"rendered":"\u4e00\u79cd\u7acb\u5f0f\u5e73\u8861\u673a\u6d4b\u91cf\u4e0d\u5e73\u8861\u91cf\u7684\u539f\u7406"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E5%89%8D%E8%A8%80\" >\u524d\u8a00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86\" >\u5de5\u4f5c\u539f\u7406<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E8%A1%A5%E5%85%85\" >\u8865\u5145<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E5%B7%A5%E8%A3%85%E6%A0%A1%E6%AD%A3\" >\u5de5\u88c5\u6821\u6b63<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E6%B5%8B%E9%87%8F%E7%9B%AE%E6%A0%87\" >\u6d4b\u91cf\u76ee\u6807<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.iyatt.com\/?p=21972\/#%E5%8D%A7%E5%BC%8F%E5%8F%8C%E9%9D%A2%E5%8A%A8%E5%B9%B3%E8%A1%A1%E6%9C%BA\" >\u5367\u5f0f\u53cc\u9762\u52a8\u5e73\u8861\u673a<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E5%89%8D%E8%A8%80\"><\/span>\u524d\u8a00<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u53bb\u5e74 11 \u6708\u7684\u65f6\u5019\uff0c\u6211\u770b\u4e86\u516c\u53f8\u91cc\u4e00\u53f0\u7acb\u5f0f\u5e73\u8861\u673a\u7684\u6280\u672f\u8bf4\u660e\uff0c\u641e\u61c2\u4e86\u6d4b\u91cf\u539f\u7406\uff0c\u7136\u540e\u7f16\u5236\u4e86\u4f5c\u4e1a\u6307\u5bfc\u4e66\uff0c\u7ea0\u6b63\u4e86\u8f66\u95f4\u73b0\u573a\u7684\u64cd\u4f5c\u3002<\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86\"><\/span>\u5de5\u4f5c\u539f\u7406<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u901a\u8fc7\u6d4b\u91cf\u632f\u52a8\u5927\u5c0f\u548c\u632f\u52a8\u7684\u89d2\u5ea6\u8ba1\u7b97\u51fa\u4e0d\u5e73\u8861\u91cf\u548c\u89d2\u5ea6\u3002<\/p>\n<p>1.\u7269\u7406\u91cf\uff1a\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\u548c\u89d2\u5ea6 <code class=\"katex-inline\">\\vec{W}<\/code>\uff0c\u4f20\u611f\u5668\u8bfb\u53d6\u7684\u632f\u52a8\u5927\u5c0f\u548c\u65b9\u5411 <code class=\"katex-inline\">\\vec{V}<\/code><\/p>\n<p>2.\u5148\u5047\u5b9a\u4e00\u4e2a\u524d\u63d0\uff0c\u5728\u8f74\u627f\u521a\u5ea6\u8db3\u591f\uff0c\u4e14\u8f6c\u901f\u4f4e\u4e8e\u4e34\u754c\u8f6c\u901f\u65f6\uff0c\u4e3b\u8f74\u8f6c\u901f\u548c\u4e3b\u8f74\u7684\u632f\u52a8\u5927\u5c0f\u53ef\u4ee5\u770b\u505a\u7ebf\u6027\u76f8\u5173\u3002<br \/>\n\u2460\u90a3\u4e48\u6709 <code class=\"katex-inline\">\\vec{W}=K\\vec{V}-\\vec W_f<\/code>\uff0c<code class=\"katex-inline\">K<\/code>\u4e3a\u4e00\u4e2a\u5e38\u6570\uff0c\u53d7\u8f6c\u901f\u7b49\u56e0\u7d20\u5f71\u54cd\uff0c\u901a\u8fc7\u65e0\u91cd\u548c\u52a0\u91cd\u6d4b\u8bd5\u53ef\u4ee5\u8ba1\u7b97\u51fa\u3002<br \/>\n\u2461<code class=\"katex-inline\">\\vec W_f<\/code>\u4e5f\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u5b83\u662f\u5de5\u88c5\u81ea\u8eab\u5bfc\u81f4\u7684\u4e0d\u5e73\u8861\u91cf\u3002\u6bd4\u5982\u5de5\u88c5\u7ed3\u6784\u4e0a\u8d28\u5fc3\u4e0d\u5728\u65cb\u8f6c\u4e2d\u5fc3\uff0c\u4ee5\u53ca\u5de5\u4ef6\u4e0e\u5de5\u88c5\u63a5\u89e6\u7684\u5b9a\u4f4d\u8f74\u4e0e\u65cb\u8f6c\u4e2d\u5fc3\u4e0d\u540c\u8f74\u3002\u5728\u5de5\u88c5\u7ed3\u6784\u4fee\u6539\uff0c\u5de5\u88c5\u53d1\u751f\u62c6\u5378\u5b89\u88c5\u540e\uff0c\u90fd\u9700\u8981\u8fdb\u884c\u5939\u5177\u8865\u507f\u4ee5\u8ba1\u7b97\u51fa\u8fd9\u4e2a\u5e38\u91cf\u3002<\/p>\n<p>3.\u6807\u5b9a\uff1a<br \/>\n\u2460\u5c06\u5de5\u4ef6\u88c5\u4e0a\uff0c\u7136\u540e\u542f\u52a8\u65e0\u8bd5\u91cd\u6d4b\u8bd5\uff0c\u6d4b\u5f97\u632f\u52a8<code class=\"katex-inline\">\\vec{V_1}<\/code>\uff0c\u5373\u6709<code class=\"katex-inline\">\\vec W_1=K\\vec V_1-\\vec W_f<\/code>\u3002<code class=\"katex-inline\">\\vec W_1<\/code>\u662f<code class=\"katex-inline\">\\vec V_1<\/code>\u632f\u52a8\u5bf9\u5e94\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u6b64\u65f6\u672a\u77e5\uff1b<code class=\"katex-inline\">\\vec W_f<\/code>\u662f\u5939\u5177\u5bfc\u81f4\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u6b64\u65f6\u672a\u77e5\u3002<br \/>\n\u2461\u5728\u8f6f\u4ef6\u8bbe\u5b9a\u7684\u534a\u5f84\u548c\u89d2\u5ea6 <code class=\"katex-inline\">\\vec R<\/code> \u5904\u52a0\u8bd5\u91cd\uff0c\u8bd5\u91cd\u8d28\u91cf m \u514b\uff0c\u518d\u6c14\u52a8\u52a0\u8bd5\u91cd\u6d4b\u8bd5\uff0c\u6d4b\u5f97\u632f\u52a8 <code class=\"katex-inline\">\\vec V_2<\/code>\uff0c\u5219\u6709 <code class=\"katex-inline\">\\vec W_1+m\\vec R=K\\vec V_2-\\vec W_f<\/code>\u3002\u6b64\u65f6\u8054\u7acb\u65e0\u8bd5\u91cd\u6d4b\u8bd5\u548c\u52a0\u8bd5\u91cd\u6d4b\u8bd5\u7684\u65b9\u7a0b\u3002\u4e00\u822c\u52a0\u8bd5\u91cd\u7528\u7684\u5df2\u77e5\u8d28\u91cf\u7684\u78c1\u94c1\u7c98\u5728\u6307\u5b9a\u65cb\u8f6c\u534a\u5f84\u3001\u89d2\u5ea6\u7684\u4f4d\u7f6e.<\/p>\n<pre><code class=\"language-katex\">\\left \\{\n\\begin{array}{l}\n\\vec W_1=K\\vec V_1\\vec-W_f\\\\\n\\vec W_1+m\\vec R=K\\vec V_2-\\vec W_f\n\\end{array}\n\\right.<\/code><\/pre>\n<p>\u5373\u6709<code class=\"katex-inline\">\\vec K=\\frac{m\\vec R_1}{\\vec V_2-\\vec V_1}<\/code><\/p>\n<p>4.\u5939\u5177\u8865\u507f\u3002\u5939\u5177\u8865\u507f\u4e00\u822c\u7528\u4e24\u70b9\u8865\u507f\u548c\u4e09\u70b9\u8865\u507f\uff0c\u4efb\u9009\u4e00\u79cd\u3002\u4e24\u70b9\u8865\u507f\u5c31\u662f\u88c5\u4e0a\u5de5\u4ef6\u542f\u52a8\u4e00\u6b21\u5939\u5177\u8865\u507f\u6d4b\u8bd5\uff0c\u518d\u5c06\u5de5\u4ef6\u65cb\u8f6c180\u00b0\u518d\u542f\u52a8\u4e00\u6b21\u5939\u5177\u8865\u507f\u6d4b\u8bd5\uff08\u4e09\u70b9\u5c31\u662f\u6d4b\u4e09\u6b21\uff0c\u6bcf\u6d4b\u4e00\u6b21\u8f6c120\u00b0\uff09\u3002<\/p>\n<p>\u4ee5\u4e24\u70b9\u8865\u507f\u6765\u8bf4\u660e\uff1a<br \/>\n\u7b2c\u4e00\u6b21\u8865\u507f\u6d4b\u8bd5\uff0c\u6d4b\u5f97\u632f\u52a8<code class=\"katex-inline\">\\vec V_{0\u00b0}<\/code>\uff0c\u8bbe\u5de5\u4ef6\u7684\u4e0d\u5e73\u8861\u91cf\u662f<code class=\"katex-inline\">\\vec Wg<\/code>\uff0c\u90a3\u4e48\u6709<code class=\"katex-inline\">K\\vec V_{0\u00b0}=\\vec W_g+\\vec W_f<\/code><br \/>\n\u5de5\u4ef6\u65cb\u8f6c180\u00b0\u540e\u518d\u6b21\u6d4b\u5f97\u632f\u52a8<code class=\"katex-inline\">\\vec V_{180\u00b0}<\/code>\uff0c\u8fd9\u4e2a\u65f6\u5019\u5de5\u4ef6\u7684\u4e0d\u5e73\u8861\u91cf\u5c31\u662f<code class=\"katex-inline\">-\\vec W_g<\/code>\uff0c\u521a\u597d\u53cd\u5411\uff0c\u90a3\u4e48\u6709<code class=\"katex-inline\">K\\vec V_{180\u00b0}=-\\vec W_g+\\vec W_f<\/code><\/p>\n<pre><code class=\"language-katex\">\\left \\{\n\\begin{array}{l}\nK\\vec V_{0\u00b0}=\\vec W_g+\\vec W_f\\\\\nK\\vec V_{180\u00b0}=-\\vec W_g+\\vec W_f\n\\end{array}\n\\right.<\/code><\/pre>\n<p>\u5373\u6709<code class=\"katex-inline\">\\vec W_f=\\frac{K(\\vec V_{0\u00b0}+\\vec V_{180\u00b0})}{2}<\/code><\/p>\n<p>5.\u8fd9\u6837\u5c31\u5f97\u5230\u4e86\u4e3b\u8f74\u632f\u52a8\u5927\u5c0f\u548c\u5de5\u4ef6\u4e0d\u5e73\u8861\u91cf\u7684\u5173\u7cfb\u4e3a<code class=\"katex-inline\">W=\\frac{m\\vec R_1}{\\vec V_2-\\vec V_1}V-\\frac{K(\\vec V_{0\u00b0}+\\vec V_{180\u00b0})}{2}<\/code><\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E8%A1%A5%E5%85%85\"><\/span>\u8865\u5145<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E5%B7%A5%E8%A3%85%E6%A0%A1%E6%AD%A3\"><\/span>\u5de5\u88c5\u6821\u6b63<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b9e\u8df5\u4e2d\uff0c\u901a\u5e38\u8981\u5c3d\u53ef\u80fd\u4fdd\u8bc1\u5de5\u88c5\u81ea\u8eab\u7684\u4e0d\u5e73\u8861\u91cf\u503c\u5c0f\uff0c\u8fd9\u6837\u6d4b\u91cf\u7ed3\u679c\u66f4\u51c6\u786e\u3002\u8fd9\u4e2a\u6d4b\u91cf\u539f\u7406\u662f\u5047\u5b9a\u4e86\u201c\u5728\u8f74\u627f\u521a\u5ea6\u8db3\u591f\uff0c\u4e14\u8f6c\u901f\u4f4e\u4e8e\u4e34\u754c\u8f6c\u901f\u201d\uff0c\u5982\u679c\u5de5\u88c5\u672c\u8eab\u4e0d\u5e73\u8861\u8fc7\u5927\uff0c\u8f74\u627f\u7684\u521a\u5ea6\u6216\u8bb8\u5c31\u4e0d\u591f\u4e86\uff0c\u6b64\u65f6\u5c31\u6210\u4e86\u6320\u6027\u8f6c\u5b50\u4e86\u3002\u8bbe\u8ba1\u5de5\u88c5\u7684\u65f6\u5019\u5c31\u8981\u8003\u8651\u5bf9\u79f0\u7ed3\u6784\uff0c\u5982\u679c\u5b9e\u5728\u65e0\u6cd5\u505a\u5230\u5bf9\u79f0\u7ed3\u6784\uff0c\u5728\u5de5\u88c5\u505a\u51fa\u6765\u540e\uff0c\u53ef\u4ee5\u5148\u5bf9\u5de5\u88c5\u6d4b\u4e0d\u5e73\u8861\u91cf\uff0c\u6b64\u65f6\u5c06\u5de5\u88c5\u89c6\u4f5c\u5de5\u4ef6\u8fdb\u884c\u68c0\u6d4b\uff0c\u5e76\u91c7\u7528\u52a0\u91cd\u6216\u53bb\u91cd\u7684\u65b9\u5f0f\u8fdb\u884c\u5de5\u88c5\u6821\u6b63\u3002<\/p>\n<p>\u5728\u6211\u51fa\u4f5c\u4e1a\u6307\u5bfc\u4e66\u4ee5\u524d\uff0c\u6211\u770b\u5230\u7684\u5de5\u4eba\u64cd\u4f5c\u5c31\u662f\u4e00\u987f\u778e\u641e\uff0c\u6807\u5b9a\u3001\u5939\u5177\u8865\u507f\u548c\u5de5\u88c5\u6821\u6b63\u6df7\u6742\u5728\u4e00\u8d77\u64cd\u4f5c\u3002\u90a3\u65f6\u5019\u6211\u624d\u8fdb\u516c\u53f8\u4e94\u4e2a\u6708\u591a\u70b9\uff0c\u524d\u9762\u90a3\u6bb5\u65f6\u95f4\u6211\u4e5f\u4e0d\u61c2\u4e5f\u6ca1\u7ba1\u3002\u6211\u731c\u6d4b\u6700\u5f00\u59cb\u5f15\u5165\u8bbe\u5907\u65f6\u662f\u6b63\u5e38\u64cd\u4f5c\u7684\uff0c\u4f46\u662f\u540e\u9762\u51e0\u5e74\u8fc7\u53bb\uff0c\u64cd\u4f5c\u5de5\u6362\u8fc7\u4eba\uff0c\u6280\u672f\u90e8\u4e5f\u6362\u4eba\u4e86\uff0c\u6ca1\u4ea4\u63a5\u597d\uff0c\u5c31\u53d8\u6210\u4e71\u4e03\u516b\u7cdf\u4e86\u3002\u5de5\u4eba\u6bcf\u6b21\u64cd\u4f5c\u6211\u770b\u7740\u5f88\u61f5\u903c\uff0c\u628a\u78c1\u94c1\u6572\u788e\u6210\u5c0f\u9897\u7c92\uff0c\u4e00\u70b9\u4e00\u70b9\u7c98\u4e0a\u53bb\u6d4b\uff0c\u76f4\u5230\u6d4b\u8bd5\u7684\u6570\u503c\u5f88\u5c0f\uff08\u5b9e\u9645\u76f8\u5f53\u4e8e\u5728\u8fdb\u884c\u5de5\u88c5\u6821\u6b63\uff09\uff0c\u4f46\u662f\u53c8\u5939\u6742\u5728\u6807\u5b9a\u548c\u5939\u5177\u8865\u507f\u7684\u64cd\u4f5c\u529b\u8fdb\u884c\uff0c\u8fd9\u5c31\u5bfc\u81f4\u6d4b\u91cf\u7ed3\u679c\u5176\u5b9e\u90fd\u4e0d\u5bf9\uff0c\u4eca\u5929\u6d4b\u4e00\u6279\u67d0\u5de5\u4ef6\u7684\u4e0d\u5e73\u8861\u91cf\u7ed3\u679c\u5f88\u5dee\uff0c\u8fc7\u51e0\u5929\u6d4b\u4e00\u6279\u51fa\u6765\u53c8\u5f88\u597d\uff0c\u4ee5\u4e3a\u662f\u6bdb\u576f\u6216\u52a0\u5de5\u7684\u95ee\u9898\u5bfc\u81f4\u7684\uff0c\u5b9e\u9645\u662f\u56e0\u4e3a\u6bcf\u6b21\u7684\u64cd\u4f5c\u90fd\u662f\u6df7\u4e71\u968f\u673a\u7684\uff0c\u6d4b\u51fa\u6765\u7684\u7ed3\u679c\u5c31\u4e0d\u5bf9\u3002<\/p>\n<h2><span 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