## Abbildungen - Kapitel 1

 ``` 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]); ``` ``` 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]) ``` ``` 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]) ``` ``` 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); ``` ``` 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'); ```

→ Zurück zur Homepage www.dgl-buch.de

© 2008 Lars Grüne, Oliver Junge