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');
					



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