From f59670c3c661c5e87b6f141c29daa2670dc78b0e Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 17 Jan 2017 20:55:43 -0500 Subject: [PATCH] lecture 1 notebook and slides --- lecture_01/lecture_01.md | 108 ++++++++++++++++++++++++++++ lecture_01/lecture_01.pdf | Bin 0 -> 319099 bytes lecture_01/output_10_0.svg | 143 +++++++++++++++++++++++++++++++++++++ 3 files changed, 251 insertions(+) create mode 100644 lecture_01/lecture_01.md create mode 100644 lecture_01/lecture_01.pdf create mode 100644 lecture_01/output_10_0.svg 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 0000000000000000000000000000000000000000..c54f29efb484d0c493c9867e5083470b86307859 GIT binary patch literal 319099 zcmeFZ1yo#1_Ai_Sf;%C&6G(7(2@)iDaCdjt#x)5LAb4;K!QGtz!QC2Y2u|Zp1I^du z&b@Qz&HcXrtheTUYu;K@yH|IeU3Kcz`PJUL_UW^$UMNXOGO;mpqP*zN>u%|;>&`@B zr(mUUFt$b!6l9Szv$t@yq~L&Y-myqp*}9rJvq;(+xtd9snK+o52@9jRxH_8|*`auT zNr(|u>}Ev^J-o&fRCH$ovJ+L@m`dw?Y3L|TE#Hb7;z`d!P!Q!)PKM9PKQk*j zo}BL7i0`3GroT{$RhTzbBuuH})Tald%U7p*3q*W}&X=%pHb0XUL3clT`mxVh0>#YU z^lwnWau4XCJb?C)Vdvt0DE-Cb`X^|){{?7k)#M$3tZ1z_8r!-Q8PYO!@B|1reZqU{ z9UU0m_BK4v_5;qV+C}`N-BU~Koe4hHK`4s)`lM!N456y+QCtE#xmNMT#JKOW&cWj6 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