hw10 - A fig 3% V 993 =¥Wmmwmxmm Wm‘m NW ’ a , v 1...

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SSLM, ‘R‘M\£ 57 z 9 History Numerical — NAME 0 History Analytical - NAME Particle m _ _ _ _ Rigid Body time (s) time (S) 1 1 a a m .m «1 Lb E m w I I .N u n A N A N _ . _ n _ 0 _ \/ S _ S .n ( a e m m 0 .t C b C fl 1 a P E M A N _ n O m ) m ,6 p m e o .m C t y d O B d .1 .wo R N:\Personal\Classes\Fall ll\34O Grading\HW lO\N2.m Page 1 % NA 3 % AA? 340 Fall '11 % HW 10 Solutions Number 2 clear all;close all;clc; L; m = 3; L = 6; d : L/2; g = 9.81; set(0,'DefaultTextInterpreter','Latex') %% Integration % Parameters tstart “ 0, tstop = 16; ts = {tstart tstop]; ICs = [deg2rad(80) O deg2rad(80) 0]; % Integration options = odeset('RelTol',le—12,'AbsTol',le—12); [time,state] = ode45(@HWlONZEOM,ts,ICs,options,g,L,d); % States and Variables thetaRB = state(:,l); thetadRB = state(:,2); thetaP = state(:,3); thetadP = state(:,4); %% Analytical t = 0:.Olzl6; thetaRBA = inline('80*cos(l.566*t)'); thetaPA = inline('80*cos(l.8083*t)'); %% Plotting subplot(221) plot(t,thetaRBA(t),t,thetaPA(t),'-—') xlabel('time (S)');ylabel('$\theta$ (deg)') title('$\theta$ History Analytical — NAME’);9rid legend('Rigid Body','Particle','Location','Best') axis([0 16 —9O 90]) subplot(222) plot(time,rad2deg(thetaRB),time,rad2deg(thetaP),'——') xlabel('time (s)');ylabel('$\theta$ (deg)') title('$\theta$ History Numerical — NAME');grid legend('Rigid Body','Particle','Location','Best') axis([0 16 —90 90]) subplot(223) plot(time,rad2deg(thetaRB),t,thetaRBA(t),'——') N:\Personal\Classes\Fall ll\34O Grading\HW 10\N2.m Page 2 xlabel('time (s)');ylabel('$\theta$ (deg)') title('Rigid Body Comparison - NAME');grid legend('Numerical','Analytical','Location','Best') axis([0 16 ~90 90]) subplot<224> plot(time,rad2deg(thetaP),t,thetaPA(t),'——') xlabel('time (s)');ylabel('$\theta$ (deg)') title('Particle Comparison - NAMZ');grid legend('Numerical','Analytical','Location','Best') axis([0 16 —90 901) N:\Personal\Classes\Fall ll\34O Grading\H...\HWlON2EOM.m Page 1 function xdot = HWlONZEOM(t,x,g,L,d) % RB Model xdot(l) = x(2); xdot(2) = —(3/2)*g/L*sin(><(l) >; % Particle Model xdot(3) = x(4); xdot(4) : -(g/d)*sin(x(3)); xdot = xdot'; (24/ “sh (13mm 2 1 "" ‘ f .L a 2—1;)“ A 5« . 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hw10 - A fig 3% V 993 =¥Wmmwmxmm Wm‘m NW ’ a , v 1...

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