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Author: Miso98

vectorcal/ps8/MATLAB22.m

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+x = 0:.01:2;
+y = x.^2+(x+1).^-2;
+
+I = trapz(x,y);
+I
+
+x = 0:.2:2;
+y = x.^2+(x+1).^-2;
+I = trapz(x,y);
+I

vectorcal/ps8/MATLAB23.m

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+G = 1350;
+A = 8;
+c = 3*10^8;
+
+% definition of the orbit
+t = 0:0.001:pi/2;
+
+% parameters of the ellipse
+a = 1.5*10^11;
+b = 1.3*10^11;
+d= 10^9;
+
+% definition of the parametric curve
+x = a*cos(t);
+y = b*sin(t);
+z= d*cos(t);
+
+% velocity of the spacecraft
+velx = gradient(x,0.001);
+vely = gradient(y,0.001);
+velz= gradient(z,0.001);
+
+% magnitude of the velocity
+velmag = sqrt(velx.^2+vely.^2+velz.^2);
+
+% acceleration of the spacecraft
+accx = gradient(velx,0.001);
+accy = gradient(vely,0.001);
+accz = gradient(velz,0.001);
+% magnitude of the acceleration
+accmag = sqrt(accx.^2+accy.^2+accz.^2);
+
+% magnitude of the force due to solar radiations
+f = -1/c*G*A;
+
+% cosine of the angle between the force and the velocity  % vector
+costheta = (velx.*accx+vely.*accy+velz.*accz)./velmag./accmag;
+
+
+% computation of the work done for t between 0 and pi
+W = trapz(f*velmag.*costheta,t)

vectorcal/ps8/pset8p1a.m

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+C1=3000;
+C2=2775;
+C3=2545;
+
+n1=3.0;
+n2=2.8;
+n3=2.6;
+
+cd=.2;
+A=2;
+g=0:.001:1;
+figure 
+
+t1=0.1*C1*((g.^(n1-1))/(n1-1) + (g.^(n1+1))/(n1+1));
+x1=0.2*C1.^2*((g.^(2*n1-1))/(2*n1-1) + (g.^(2*n1+1))/(2*n1+1));
+y1=0.1*C1.^2*((g.^(2*n1-2))/(2*n1-2) + (g.^(2*n1+2))/(2*n1+2));
+plot(x1,y1,'r')
+hold on
+
+t2=0.1*C2*((g.^(n2-1))/(n2-1) + (g.^(n2+1))/(n2+1));
+x2=0.2*C2.^2*((g.^(2*n2-1))/(2*n2-1) + (g.^(2*n2+1))/(2*n2+1));
+y2=0.1*C2.^2*((g.^(2*n2-2))/(2*n2-2) + (g.^(2*n2+2))/(2*n2+2));
+plot(x2,y2,'g')
+hold on
+
+t3=0.1*C3*((g.^(n3-1))/(n3-1) + (g.^(n3+1))/(n3+1));
+x3=0.2*C3.^2*((g.^(2*n3-1))/(2*n3-1) + (g.^(2*n3+1))/(2*n3+1));
+y3=0.1*C3.^2*((g.^(2*n3-2))/(2*n3-2) + (g.^(2*n3+2))/(2*n3+2));
+plot(x3,y3,'b')
+hold on
+
+title('different trajectories of launch satellites')
+xlabel('horizontal displacement')
+ylabel('vertical displacement')
+legend('case 1','case 2', 'case 3')
+
+%part1b
+
+figure
+velx1 = gradient(x1,g).*gradient(g,t1);
+vely1 = gradient(y1,g).*gradient(g,t1);
+speed1 = (velx1.^2 + vely1.^2).^.5;
+plot(t1,speed1,'g')
+ylabel('speed1')
+xlabel('time')
+ 
+hold on
+velx2 = gradient(x2,g).*gradient(g,t2);
+vely2 = gradient(y2,g).*gradient(g,t2);
+speed2 = (velx2.^2 + vely2.^2).^.5;
+plot(t2,speed2,'b')
+ylabel('speed2')
+xlabel('time')
+
+ 
+hold on
+velx3 = gradient(x3,g).*gradient(g,t3);
+vely3 = gradient(y3,g).*gradient(g,t3);
+speed3 = (velx3.^2 + vely3.^2).^.5;
+plot(t3,speed3,'r')
+ylabel('speed')
+xlabel('time')
+legend('case 1','case 2', 'case 3')
+title('speed vs time')
+
+%part 1c
+figure
+p1=1.2.*exp(-y1./8000);
+p2=1.2.*exp(-y2./8000);
+p3=1.2.*exp(-y3./8000);
+F1 = .5*p1.*speed1.^2*A*cd;
+F2 = .5*p2.*speed2.^2*A*cd;
+F3 = .5*p3.*speed3.^2*A*cd;
+
+plot(t1,F1,'g')
+hold on
+plot(t2,F2,'r')
+hold on
+plot(t3,F3,'b')
+xlabel('time')
+ylabel('force')
+title('drag force vs time')
+legend('case 1','case 2','case 3')
+
+%part 1d
+
+work1 = -1*trapz(abs(F1).*speed1,t1)
+work2 = -1*trapz(abs(F2).*speed2,t2)
+work3 = -1*trapz(abs(F3).*speed3,t3)

vectorcal/ps8/pset8p1b.m

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+
+subplot(1,3,1)
+velx1 = gradient(x1,g).*gradient(g,t1);
+vely1 = gradient(y1,g).*gradient(g,t1);
+speed1 = (velx1.^2 + vely1.^2).^5;
+plot(speed1,t1,'g')
+ylabel('speed1')
+xlabel('time')
+title('case 1 speed vs time')
+
+subplot(1,3,2)
+velx2 = gradient(x2,g).*gradient(g,t2);
+vely2 = gradient(y2,g).*gradient(g,t2);
+speed2 = (velx2.^2 + vely2.^2).^5;
+plot(speed2,t2,'b')
+ylabel('speed2')
+xlabel('time')
+title('case 2 speed vs time')
+
+subplot(1,3,3)
+velx3 = gradient(x3,g).*gradient(g,t3);
+vely3 = gradient(y3,g).*gradient(g,t3);
+speed3 = (velx3.^2 + vely3.^2).^5;
+plot(speed3,t3,'r')
+ylabel('speed3')
+xlabel('time')
+title('case 3 speed vs time')
+
+

vectorcal/ps8/subplotte dversion pset7p1b.m

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+subplot(1,3,1)
+velx1 = gradient(x1,g).*gradient(g,t1);
+vely1 = gradient(y1,g).*gradient(g,t1);
+speed1 = (velx1.^2 + vely1.^2).^5;
+plot(t1, speed1,'g')
+ylabel('speed1')
+xlabel('time')
+title('case 1 speed vs time')
+
+subplot(1,3,2)
+velx2 = gradient(x2,g).*gradient(g,t2);
+vely2 = gradient(y2,g).*gradient(g,t2);
+speed2 = (velx2.^2 + vely2.^2).^5;
+plot(t2,speed2,'b')
+ylabel('speed2')
+xlabel('time')
+title('case 2 speed vs time')
+
+subplot(1,3,3)
+velx3 = gradient(x3,g).*gradient(g,t3);
+vely3 = gradient(y3,g).*gradient(g,t3);
+speed3 = (velx3.^2 + vely3.^2).^5;
+plot(t3,speed3,'r')
+ylabel('speed3')
+xlabel('time')
+title('case 3 speed vs time')