problem 5

Problem5.m

@@ -0,0 +1,26 @@
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',1)
+dt=0.1;
+    x=[0:dt:20]';
+    y_n=zeros(length(x),4);
+    y_n(1,:)=[10 0 0 2];
+    for i=2:length(x)
+            dy=phugoid_ode(x(i-1),y_n(i-1,:));
+            y_n(i,:)=y_n(i-1,:)+dt*dy;
+    end
+
+dt=0.01;
+    x=[0:dt:20]';
+    y_n2=zeros(length(x),4);
+    y_n2(1,:)=[10 0 0 2];
+    for i=2:length(x)
+            dy=phugoid_ode(x(i-1),y_n2(i-1,:));
+            y_n2(i,:)=y_n2(i-1,:)+dt*dy;
+    end
+    [t23,y23]=ode23(@(t,y) phugoid_ode(t,y),[0 20],[10 0 0 2]);
+    d = figure(4);
+    plot(y_n(:,3),y_n(:,4),y_n2(:,3),y_n2(:,4),y23(:,3),y23(:,4))
+    legend('Euler .1','Euler .01','ode23','Location','Northeast')
+    xlabel('Distance')
+    ylabel('Height')

README.md

@@ -137,3 +137,34 @@ function x = prob4ptC(prob4_ode, dt, x0,tlimits)
 end
 ```
 ![](assets/README-ac6c7a25.png)
+
+# Problem 5
+```
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',1)
+dt=0.1;
+    x=[0:dt:20]';
+    y_n=zeros(length(x),4);
+    y_n(1,:)=[10 0 0 2];
+    for i=2:length(x)
+            dy=phugoid_ode(x(i-1),y_n(i-1,:));
+            y_n(i,:)=y_n(i-1,:)+dt*dy;
+    end
+
+dt=0.01;
+    x=[0:dt:20]';
+    y_n2=zeros(length(x),4);
+    y_n2(1,:)=[10 0 0 2];
+    for i=2:length(x)
+            dy=phugoid_ode(x(i-1),y_n2(i-1,:));
+            y_n2(i,:)=y_n2(i-1,:)+dt*dy;
+    end
+    [t23,y23]=ode23(@(t,y) phugoid_ode(t,y),[0 20],[10 0 0 2]);
+    d = figure(4);
+    plot(y_n(:,3),y_n(:,4),y_n2(:,3),y_n2(:,4),y23(:,3),y23(:,4))
+    legend('Euler .1','Euler .01','ode23','Location','Northeast')
+    xlabel('Distance')
+    ylabel('Height')
+    ```
+    ![](assets/README-f6577255.png)

phugoid_ode.m

@@ -0,0 +1,11 @@
+function dy=phugoid_ode(t,y)
+g=9.81;
+vt=5.5;
+cl=5.2;
+cd=1;
+dy=zeros(size(y));
+dy(1)=-g*sin(y(2))-cd/cl*g/vt^2*y(1)^2;
+dy(2)=-g/y(1)*cos(y(2))+g/vt^2*y(1);
+dy(3)=y(1)*cos(y(2));
+dy(4)=y(1)*sin(y(2));
+end