{"id":3694,"date":"2026-05-27T20:31:30","date_gmt":"2026-05-27T12:31:30","guid":{"rendered":"http:\/\/81.70.49.155\/?p=3694"},"modified":"2026-05-27T20:31:30","modified_gmt":"2026-05-27T12:31:30","slug":"matlab%e6%98%9f%e7%b3%bb%e7%9a%84%e5%bd%a2%e6%88%90%e6%a8%a1%e6%8b%9f","status":"publish","type":"post","link":"http:\/\/81.70.49.155\/?p=3694","title":{"rendered":"[MATLAB]\u661f\u7cfb\u7684\u5f62\u6210\u6a21\u62df"},"content":{"rendered":"

\n\t\"\"\n<\/p>\n

\n
\n\t\t\tclc<\/span>\n\t\t<\/div>\n
\n\t\t\tclear<\/span>\n\t\t<\/div>\n
\n\t\t\tclose all<\/span><\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t%% \u7269\u7406\u4e0e\u6a21\u62df\u53c2\u6570\uff08\u5df2\u4f18\u5316\u4e3a\u661f\u7cfb\u53c2\u6570\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tG = 1.0; % \u5f15\u529b\u5e38\u6570\uff08\u8c03\u5927\u8ba9\u5f15\u529b\u66f4\u660e\u663e\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\trho = 0.001; % \u5bc6\u5ea6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tNp = 150; % \u661f\u4f53\u6570\u91cf<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tdt = 0.1; % \u65f6\u95f4\u6b65\u957f\uff08\u66f4\u5c0f\u66f4\u7a33\u5b9a\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\ttotalSteps = 50000; % \u603b\u6b65\u6570<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tdrawStep =200; % \u7ed8\u56fe\u95f4\u9694<\/span><\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t%% \u8fb9\u754c\uff08\u56fa\u5b9a\u4e3a\u53ef\u89c6\u8303\u56f4\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tlim = 200;<\/span>\n\t\t<\/div>\n
\n\t\t\tliml = -lim;<\/span>\n\t\t<\/div>\n
\n\t\t\tlimu = lim;<\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t%% 1. \u521d\u59cb\u5316\uff1a\u661f\u7cfb\u6838\u5fc3+\u65cb\u8f6c\u901f\u5ea6\uff08\u5173\u952e\uff01\u661f\u7cfb\u5fc5\u987b\u6709\u5207\u5411\u65cb\u8f6c\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tXa = zeros(Np, 2); % \u4f4d\u7f6e<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tU = zeros(Np, 2); % \u901f\u5ea6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tR = rand(Np, 1)*1.5 + 2; % \u661f\u4f53\u534a\u5f84<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tM = rho * pi * R.^2; % \u8d28\u91cf<\/span><\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t% \u751f\u6210\u5706\u76d8\u72b6\u521d\u59cb\u5206\u5e03\uff08\u661f\u7cfb\u662f\u5706\u76d8\uff0c\u4e0d\u662f\u968f\u673a\u65b9\u5757\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tfor <\/span>i = 1:Np<\/span>\n\t\t<\/div>\n
\n\t\t\t r = (rand()+0.5) * 100; % \u5f84\u5411\u8ddd\u79bb<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t theta = rand() * 2*pi; % \u89d2\u5ea6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t Xa(i,1) = r * cos(theta);<\/span>\n\t\t<\/div>\n
\n\t\t\t Xa(i,2) = r * sin(theta);<\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % \u5173\u952e\uff1a\u7ed9\u521d\u59cb\u65cb\u8f6c\u901f\u5ea6\uff08\u5f00\u666e\u52d2\u65cb\u8f6c\uff0c\u661f\u7cfb\u5f62\u6210\u7684\u6838\u5fc3\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t v = sqrt(G * sum(M) \/ (r + 10)); % \u8f68\u9053\u901f\u5ea6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t U(i,1) = -v * sin(theta); % \u5207\u5411\u901f\u5ea6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t U(i,2) = v * cos(theta);<\/span>\n\t\t<\/div>\n
\n\t\t\tend<\/span><\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t%% 2. \u6a21\u62df\u4e3b\u5faa\u73af<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tfor <\/span>tStep = 1:totalSteps<\/span>\n\t\t<\/div>\n
\n\t\t\t Ac = zeros(Np, 2); % \u52a0\u901f\u5ea6\u5f52\u96f6<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % N\u4f53\u5f15\u529b\u8ba1\u7b97\uff08\u4f18\u5316\u4e86\u8ddd\u79bb\u3001\u8f6fening\u3001\u529b\u8ba1\u7b97\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t for <\/span>i = 1:Np<\/span>\n\t\t<\/div>\n
\n\t\t\t for <\/span>j = i+1:Np<\/span>\n\t\t<\/div>\n
\n\t\t\t % \u4f4d\u7f6e\u5dee<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t dx = Xa(i,1) - Xa(j,1);<\/span>\n\t\t<\/div>\n
\n\t\t\t dy = Xa(i,2) - Xa(j,2);<\/span>\n\t\t<\/div>\n
\n\t\t\t distSq = dx^2 + dy^2;<\/span>\n\t\t<\/div>\n
\n\t\t\t dist = sqrt(distSq);<\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % \u8f6fening\u957f\u5ea6\uff1a\u9632\u6b62\u8ddd\u79bb\u4e3a0\u5bfc\u81f4\u7206\u70b8\uff08\u5173\u952e\u4fee\u590d\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t softening = 2;<\/span>\n\t\t<\/div>\n
\n\t\t\t dist = max(dist, softening);<\/span>\n\t\t<\/div>\n
\n\t\t\t disR=R(i)+R(j)+0.5;<\/span>\n\t\t<\/div>\n
\n\t\t\t % \u4e07\u6709\u5f15\u529b\u516c\u5f0f<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t if <\/span>dist>disR<\/span>\n\t\t<\/div>\n
\n\t\t\t F = G * M(i) * M(j) \/ dist^2;<\/span>\n\t\t<\/div>\n
\n\t\t\t else<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t F=-0.0001\/abs((dist-R(i)-R(j)-1));<\/span>\n\t\t<\/div>\n
\n\t\t\t end<\/span><\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t % \u5355\u4f4d\u5411\u91cf<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t fx = dx \/ dist;<\/span>\n\t\t<\/div>\n
\n\t\t\t fy = dy \/ dist;<\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % \u52a0\u901f\u5ea6\u66f4\u65b0<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t Ac(i,1) = Ac(i,1) - F\/M(i) * fx;<\/span>\n\t\t<\/div>\n
\n\t\t\t Ac(i,2) = Ac(i,2) - F\/M(i) * fy;<\/span>\n\t\t<\/div>\n
\n\t\t\t Ac(j,1) = Ac(j,1) + F\/M(j) * fx;<\/span>\n\t\t<\/div>\n
\n\t\t\t Ac(j,2) = Ac(j,2) + F\/M(j) * fy;<\/span>\n\t\t<\/div>\n
\n\t\t\t end<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t end<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % 3. \u901f\u5ea6 + \u4f4d\u7f6e\u66f4\u65b0\uff08\u6b27\u62c9\u79ef\u5206\uff0c\u52a0\u6781\u5f31\u963b\u5c3c\u4fdd\u6301\u7a33\u5b9a\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t damping = 0.9999;<\/span>\n\t\t<\/div>\n
\n\t\t\t U = U * damping + Ac * dt;<\/span>\n\t\t<\/div>\n
\n\t\t\t Xa = Xa + U * dt;<\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % 4. \u8fb9\u754c\uff1a\u4e0d\u5faa\u73af\uff01\u76f4\u63a5\u56fa\u5b9a\u53ef\u89c6\u8303\u56f4\uff08\u661f\u7cfb\u4e0d\u4f1a\u4e71\u8dd1\uff09<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t Xa(Xa > limu) = limu;<\/span>\n\t\t<\/div>\n
\n\t\t\t Xa(Xa < liml) = liml;<\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t % 5. \u5b9e\u65f6\u7ed8\u56fe<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t if <\/span>mod(tStep, drawStep) == 0<\/span>\n\t\t<\/div>\n
\n\t\t\t clf; hold on<\/span>; axis equal<\/span>; axis off<\/span>;<\/span>\n\t\t<\/div>\n
\n\t\t\t set(gcf,'Color'<\/span>,[0.1 0.1 0.2]); % \u9ed1\u8272\u80cc\u666f\u66f4\u50cf\u5b87\u5b99<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t set(gca, ...<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t 'XLim'<\/span>, [liml,limu], ...<\/span> % X \u8f74\u663e\u793a\u8303\u56f4<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t 'YLim'<\/span>, [liml,limu]); % Y \u8f74\u663e\u793a\u8303\u56f4<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t % \u7ed8\u5236\u6240\u6709\u661f\u4f53<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t for <\/span>i = 1:Np<\/span>\n\t\t<\/div>\n
\n\t\t\t ang = 0:0.1:2*pi;<\/span>\n\t\t<\/div>\n
\n\t\t\t xCircle = Xa(i,1) + R(i)*cos(ang);<\/span>\n\t\t<\/div>\n
\n\t\t\t yCircle = Xa(i,2) + R(i)*sin(ang);<\/span>\n\t\t<\/div>\n
\n\t\t\t fill(xCircle, yCircle, [1,1,0.8], 'EdgeColor'<\/span>,'none'<\/span>);<\/span>\n\t\t<\/div>\n
\n\t\t\t end<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t <\/span>\n\t\t<\/div>\n
\n\t\t\t hold off<\/span>;<\/span>\n\t\t<\/div>\n
\n\t\t<\/div>\n
\n\t\t\t export_fig(gcf,'-png'<\/span>, '-r300'<\/span>, '-opengl'<\/span>, ['PNG\/'<\/span>,num2str(100000+tStep),'.png'<\/span>],'-nocrop'<\/span>);<\/span>\n\t\t<\/div>\n
\n\t\t\t % drawnow;<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\t end<\/span><\/span>\n\t\t<\/div>\n
\n\t\t\tend<\/span><\/span>\n\t\t<\/div>\n<\/p><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"

clc clear close all %% \u7269\u7406\u4e0e\u6a21\u62df\u53c2\u6570\uff08\u5df2\u4f18\u5316\u4e3a\u661f\u7cfb\u53c2\u6570\uff09 G = 1.0; % \u5f15\u529b\u5e38 … \u7ee7\u7eed\u9605\u8bfb\u201c[MATLAB]\u661f\u7cfb\u7684\u5f62\u6210\u6a21\u62df\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"views":13,"_links":{"self":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3694"}],"collection":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3694"}],"version-history":[{"count":1,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3694\/revisions"}],"predecessor-version":[{"id":3696,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3694\/revisions\/3696"}],"wp:attachment":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3694"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}