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t = 0:0.05:4;
xt = diag([0:0.1:2])*repmat(exp(t),21,1);
h = plot(t,xt,'k');
axis([-0.1,4,-0.1,6]);
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g=9.81;
[x,y] = meshgrid(-1.2*pi:0.4:1.2*pi,-6*pi:0.8:6*pi);
u = y;
v = -g*sin(x);
h = quiver(x,y,u,v,1.75,'k');
axis([-1.2*pi 1.2*pi -8 8])
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g = 9.81;
[x,y] = meshgrid(-1.2*pi:0.4:1.2*pi,-6*pi:0.8:6*pi)
u = y;
v = -g*sin(x);
clf; hold on;
h=plot([-pi,0,pi],0,'k.');
pdl = inline('[x(2);-9.81*sin(x(1))]','t','x');
opt=odeset('RelTol',1e-5);
[t,x]=ode45(pdl,[0 10],[1.5;0],opt);
h=plot(x(:,1),x(:,2),'k-');
[t,x]=ode45(pdl,[0 10],[-1.2*pi;4.0],opt);
h=plot(x(:,1),x(:,2),'k-');
[t,x]=ode45(pdl,[0 5],[-pi;1e-3],opt);
h=plot(x(:,1),x(:,2),'k-');
axis([-1.2*pi 1.2*pi -8 8])
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sigma = 10; beta=8/3; rho=28;
dgl = inline('[10*(x(2)-x(1)); 28*x(1)-x(2)-x(1)*x(3); x(1)*x(2)-8/3*x(3)]','t','x');
opt = odeset('RelTol',1e-5);
x0=[1;1;1];
[t,x1]=ode45(dgl,[0,100],x0,opt);
h=plot3(x1(:,1),x1(:,2),x1(:,3),'k');
view(45,25);
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sigma = 10; beta=8/3; rho=28;
dgl = inline('[10*(x(2)-x(1)); 28*x(1)-x(2)-x(1)*x(3); x(1)*x(2)-8/3*x(3)]','t','x');
opt = odeset('RelTol',1e-5);
x01=[1;1;1];
[t1,x1]=ode45(dgl,[0,40],x01,opt);
x02=[1+1e-6;1;1];
[t2,x2]=ode45(dgl,[0,40],x02,opt);
h=plot(t2,x2(:,1),'Color',[0.6 0.6 0.6]);
hold on
h=plot(t1,x1(:,1),'k');
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