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function dy=rigid4(t,y)
w=78;%ÂÖÌ¥µÄתËÙ
R=0.317;%ÂÖÌ¥°ë¾¶
u=10;%Íâ½ç·çËÙ
ls=1.225;%¿ÕÆøÃܶÈ
lg=2.5*10^3;%Ä¥Á£ÃܶÈ
d=10^(-5);%Ä¥Á£Ö±¾¶
g=9.806;%ÖØÁ¦¼ÓËÙ¶È
m=1.79*10^(-5);%¿ÕÆø¶¯Á¦Õ³¶È
n=m/ls;%Ô˶¯Õ³¶È
k=3*ls/(4*lg*d);
g1=(1-ls/lg)*g;
dy=zeros(4,1);%Ò»¸öÁÐÏòÁ¿
V=sqrt(y(2)^2+y(4)^2);
u0=w*R^2/(R+y(1));
U1=(0.32*y(1)*u^1.5*n*y(3)-0.005*y(1)^3*u^2.5)/(n^1.5*y(3)^1.5)+u0;
U2=(0.08*n*y(1)^2*u^1.5*y(3)-0.002*y(1)^4*u^2.5)/(n^1.5*y(3)^2.5);
U=sqrt(U1^2+U2^2);
Re=ls*d*abs(U-V)/m;
Cd=19.5/Re^0.633;
dy(1)=y(2);
dy(3)=y(4);
dy(2)=k*Cd*abs(U2-y(2))*(U2-y(2));
dy(4)=-g1+k*Cd*abs(U1-y(4))*(U1-y(4));
dy=[dy(1) dy(2) dy(3) dy(4)]';
end
ÉÏÃæÊÇÖ÷³ÌÐò£¬ÏÂÃæÊÇÃüÁî´°¿ÚÖеijÌÐò
tspan=linspace(0,1,1000);
[t,y]=ode45(@rigid4,tspan,[0 2.3 0 2.1]);
plot(y(:,1),y(:,3))
axis([0 0.003 0 1])
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function dy=rigid4(t,y)
w=78;%ÂÖÌ¥µÄתËÙ
R=0.317;%ÂÖÌ¥°ë¾¶
u=10;%Íâ½ç·çËÙ
ls=1.225;%¿ÕÆøÃܶÈ
lg=2.5*10^3;%Ä¥Á£ÃܶÈ
d=10^(-5);%Ä¥Á£Ö±¾¶
g=9.806;%ÖØÁ¦¼ÓËÙ¶È
m=1.79*10^(-5);%¿ÕÆø¶¯Á¦Õ³¶È
n=m/ls;%Ô˶¯Õ³¶È
k=3*ls/(4*lg*d);
g1=(1-ls/lg)*g;
dy=zeros(4,1);%Ò»¸öÁÐÏòÁ¿
V=sqrt(y(2)^2+y(4)^2);
u0=w*R^2/(R+y(1));
U1=(0.32*y(1)*u^1.5*n*y(3)-0.005*y(1)^3*u^2.5)/(n^1.5*y(3)^1.5)+u0;%%%% U1=NAN ÓÐÎÊÌ⣬ÎÊÌâÔÚÓÚy(3)=0,×ö³ýÊýÁË
U2=(0.08*n*y(1)^2*u^1.5*y(3)-0.002*y(1)^4*u^2.5)/(n^1.5*y(3)^2.5);%%% ͬÑù£¬U2=NAN£¬Ò²ÓÉÓÚy(3)=0,ÔÚ·ÖĸÉÏ
U=sqrt(U1^2+U2^2); % NAN
Re=ls*d*abs(U-V)/m;% NAN
Cd=19.5/Re^0.633;% NAN
dy(1)=y(2);
dy(3)=y(4);
dy(2)=k*Cd*abs(U2-y(2))*(U2-y(2)); %NAN
dy(4)=-g1+k*Cd*abs(U1-y(4))*(U1-y(4));% NAN

end


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