lecture 1 notebook and slides

lecture_01/lecture_01.md

@@ -0,0 +1,108 @@
+
+# Freefall Model
+## Octave solution (will run same on Matlab)
+
+
+```octave
+%plot --format svg
+```
+
+
+```octave
+set (0, "defaultaxesfontname", "Helvetica")
+set (0, "defaultaxesfontsize", 18)
+set (0, "defaulttextfontname", "Helvetica")
+set (0, "defaulttextfontsize", 18) 
+set (0, "defaultlinelinewidth", 4)
+```
+
+Define time from 0 to 12 seconds
+
+
+```octave
+t=[0,2,4,6,8,10,12]'
+```
+
+    t =
+
+        0
+        2
+        4
+        6
+        8
+       10
+       12
+
+
+
+Define constants and analytical solution (meters-kilogram-sec)
+
+
+```octave
+c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);
+
+v_analytical = v_terminal*tanh(g*t/v_terminal)
+```
+
+    v_analytical =
+
+        0.00000
+       18.61630
+       32.45521
+       40.64183
+       44.84646
+       46.84974
+       47.77002
+
+
+
+
+```octave
+v_numerical=zeros(length(t),1);
+for i=1:length(t)-1
+    v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*2;
+end
+v_numerical
+```
+
+    v_numerical =
+
+        0.00000
+       19.62000
+       36.03213
+       44.83284
+       47.70298
+       48.35986
+       48.49089
+
+
+
+Display time, velocity (analytical) and velocity (numerical)
+
+
+```octave
+fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
+fprintf('-----------------------------------------------')
+M=[t,v_analytical,v_numerical];
+fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');
+```
+
+    time (s)|vel analytical (m/s)|vel numerical (m/s)
+    -----------------------------------------------
+        0.0 |               0.00 |            0.00
+        2.0 |              18.62 |           19.62
+        4.0 |              32.46 |           36.03
+        6.0 |              40.64 |           44.83
+        8.0 |              44.85 |           47.70
+       10.0 |              46.85 |           48.36
+       12.0 |              47.77 |           48.49
+
+
+
+```octave
+plot(t,v_analytical,'-',t,v_numerical,'o-')
+```
+
+
+![svg](output_10_0.svg)
+