falling chain
DESCRIPTION
Falling Chain. Luu Chau Kayla Chau Jonathan Bernal. On the paradox of the free falling folded chain M.Schagerl A. Steindl W. Steiner H. Troger Dr. Tyler McMillen. Reference. speed=1; % speed of falling chain (1_slow 100_fast) T=1; % time of calculations (secs) - PowerPoint PPT PresentationTRANSCRIPT
ReferenceReference
On the paradox of the free falling folded chain M.Schagerl A. Steindl W. Steiner H. Troger
Dr. Tyler McMillen
Initial Condition for ParametersInitial Condition for Parametersspeed=1; % speed of falling chain (1_slow 100_fast)T=1; % time of calculations (secs)n=7; % number of links (must be odd number)frames=5; % number of frames per TM=15; % total mass of the chainL=2; % length of the chain (meters)m=1; % mass attached to end of chaina=.00475; % length of linkb=.0025; % width of linke=b/a; % ratio h=L/n; % distance between two jointsmu=M/n; % mass of each linkg=9.81; % gravitytimes=linspace(0,T,frames); % number of moments
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initial=[zeros(1,(n-1)/2) pi/2 ones(1,(n-1)/2)*pi zeros(1,n)];
initial = 0 0 0 1.5708 3.1416 3.1416 3.1416 0 0 0 0 0 0 0
Initialize Condition for ChainInitialize Condition for Chain
Calculate Moments of InertiaCalculate Moments of InertiaIy=((mu*h^2)/12)*(2*a/h)^2*(1+3*e)/(1+e); %moment of
inertiaIz=((mu*h^2)/12)*(2*a/h)^2*(1+e)^2; %moment
of inertia for i=1:n for j=1:n G(i,j)=(M/mu)*h+n*h-(max(i,j)-0.5)*h;
%nxn matrix, equations of motion end if (i/2)==(i-ceil(i/2)) %if “i” is even I(i)=Iz; else %if “i” is odd I(i)=Iy; endend
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ODE outputODE output
t = phi = 0 0 0 0 1.5708 3.1416 3.1416 3.1416 0.2500 -0.0442 0.0491 0.2926 0.3162 2.5375 3.3701 3.0859 0.5000 0.0887 0.0322 0.3209 0.0319 -0.1541 0.9014 3.2265
0.7500 -0.5014 1.4469 0.0484 -1.4148 0.3501 0.3505 -0.1128 1.0000 -0.0366 -0.5347 0.2591 -1.1734 2.4062 3.1726 -0.9964
Compute Coordinates of Each JointCompute Coordinates of Each Joint
for i=1:frames for j=2:n+1 x(i,j)=x(i,j)+h*sum(sin(phi(i,1:j-1))); y(i,j)=y(i,j)-h*sum(cos(phi(i,1:j-1))); endend
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OutputOutput
x = 0 0 0 0 0.2857 0.2857 0.2857 0.2857 0 -0.0126 0.0014 0.0838 0.1726 0.3349 0.2702 0.2861 0 0.0253 0.0345 0.1247 0.1338 0.0899 0.3140 0.2897 0 -0.1373 0.1462 0.1600 -0.1222 -0.0242 0.0739 0.0417 0 -0.0105 -0.1561 -0.0829 -0.3463 -0.1546 -0.1635 -0.4034
y = 0 -0.2857 -0.5714 -0.8571 -0.8571 -0.5714 -0.2857 0 0 -0.2854 -0.5708 -0.8444 -1.1159 -0.8808 -0.6025 -0.3172 0 -0.2846 -0.5702 -0.8413 -1.1269 -1.4092 -1.5865 -1.3018 0 -0.2505 -0.2859 -0.5712 -0.6156 -0.8840 -1.1524 -1.4363 0 -0.2855 -0.5314 -0.8075 -0.9181 -0.7062 -0.4206 -0.5759
Plot MoviePlot Moviefor i=1:frames plot(x(i,:),y(i,:),'.-') %chain hold on plot(x(i,n+1),y(i,n+1),'o','MarkerFaceColor','r','MarkerSize',8)
%end of chain plot(xball,yball(i),'o','MarkerFaceColor','g','MarkerSize',9) %falling object axis([-2 2 -L 0]) mov(i)=getframe; hold off endmovie(mov,2,speed)