diff --git a/lecture_01/lecture_01.md b/lecture_01/lecture_01.md new file mode 100644 index 0000000..b347272 --- /dev/null +++ b/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) + diff --git a/lecture_01/lecture_01.pdf b/lecture_01/lecture_01.pdf new file mode 100644 index 0000000..c54f29e Binary files /dev/null and b/lecture_01/lecture_01.pdf differ diff --git a/lecture_01/output_10_0.svg b/lecture_01/output_10_0.svg new file mode 100644 index 0000000..5c7cdea --- /dev/null +++ b/lecture_01/output_10_0.svg @@ -0,0 +1,143 @@ + + +Gnuplot +Produced by GNUPLOT 5.0 patchlevel 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0 + + + + + 10 + + + + + 20 + + + + + 30 + + + + + 40 + + + + + 50 + + + + + 0 + + + + + 2 + + + + + 4 + + + + + 6 + + + + + 8 + + + + + 10 + + + + + 12 + + + + + + + + + gnuplot_plot_1a + + + + + + gnuplot_plot_2a + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file