Abbildungen - Kapitel 2

 ``` hold on for phi=0:2*pi/20:2*pi, x0 = 3*[cos(phi);sin(phi)]; t = 0:0.05:10; xt = [exp(-t)*x0(1); exp(-3*t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); end axis(1.5*[-1,1,-1,1]); axis square ``` ``` hold on for phi=-1.5:3/10:1.5, x0 = [phi;-phi]; t = -10:0.05:10; xt = [exp(-t)*x0(1); exp(t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); x0 = [phi;phi]; t = -10:0.05:10; xt = [exp(-t)*x0(1); exp(t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); end ``` ``` hold on V=[1 0.5; 0.5 1]; for phi=0:2*pi/20:2*pi, x0 = 3*[cos(phi);sin(phi)]; t = 0:0.05:10; xt = V*[exp(-3*t)*x0(1); exp(-9*t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); end axis(1.5*[-1,1,-1,1]); axis square ``` ``` hold on V=[1 0.5; 0.5 1]; for phi=-3:3/10:3, x0 = [phi;-phi]; t = -10:0.05:10; xt = V*[exp(-t)*x0(1); exp(t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); x0 = [phi;phi]; t = -10:0.05:10; xt = V*[exp(-t)*x0(1); exp(t)*x0(2)]; h = plot(xt(1,:),xt(2,:),'k'); end ``` ``` t=linspace(0,2,1000); a=2; x=exp(a*t).*(2-t); h = plot(t,exp(a*t),'color',[0.6 0.6 0.6]); hold on; h = plot(t,x,'k'); axis([0 2 0 30]) h = legend('exp2t','exp2t(2-t)') set(h,'location','best') ``` ``` t = 0:0.05:20*pi; xt = exp((-0.04 + i)*t); % bzw. exp(i*t); bzw. exp((0.04 + i)*t); h = plot(real(xt),imag(xt),'k'); axis(1.5*[-1,1,-1,1]); axis square ``` ``` t = -4:0.05:4; xt = diag([-4:0.2:4])*repmat(exp(t.^2/2),41,1); h=plot(t,xt,'k'); axis([-2,2,-4,4]); ``` ``` t = -4:0.05:4; xt = diag([-12:0.4:12])*repmat(exp(sin(t)),61,1); h=plot(t,xt,'k'); axis([-4,4,-4,4]); ```

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