function gg303_2011_lab_10_b
F = [1 2;0 1]
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% Find and print all the remaining relevant matrices (invF,C,B,invB,U,V,R)
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% Find and print invF (leave off the semicolon at the line end)
invF = *******
% Find and print matrix C = F'F (leave off the semicolon at the line end)
C = *******
% Find and print matrix B = FF' (leave off the semicolon ...)
B = *******
% Find and print matrix invB = (invF)'invF (leave off the semicolon ...)
invB = *******
% Find and print matrix U = (C)^(1/2) (leave off the semicolon...)
U = *******
% Find and print matrix V = (B)^(1/2)(leave off the semicolon ...)
V = *******
% Find and print rotation matrix R from F and U
R = *******
% Find and print rotation matrix R_alt from V and F as a check on R
R_alt = *******

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% Find and print the eigenvectors and eigenvalues for matrices F,U,V
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% Find and print the eigenvectors (vF) and eigenvalues (dF) for F
[vF,dF] = *******
% Find and print the eigenvectors (vinvF) and eigenvalues (dinvF) for invF
[vinvF,dinvF] = *******
% Find and print the eigenvectors (vU) and eigenvalues (dU) for U
[vU,dU] = *******
% Find and print the eigenvectors (vV) and eigenvalues (dV) for V
[vV,dV] = *******

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% Retro-deform the principal strain axes (the eigenvectors of V)
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% Find and print the eigenvectors (vF) and eigenvalues (dF) for F
Rps = invF*vV

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% Set up points defining a unit circle
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% Calculate the coordinates of points around the unit circle 
% and place the x-coordinates in the first row of a matrix called X, 
% and place the y-coordinates in the second row of matrix X.
% Matrix X has initial positions.
theta = 0:pi/180:2*pi;
x = cos(theta);
y = sin(theta);
X = [x;y];

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% Calculate the positions X'(Xp) of points on the strain ellipse
% and the positions X"(Xpp) of points on the reciprocal strain ellipse
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% Calculate the positions Xp using F and X
Xp = ******* 
% Separate the x'(xp) coordinates from the first row of Xp
xp = Xp(1,:);
% Separate the y'(yp) coordinates from the second row of Xp
yp = Xp(2,:);

% Calculate the positions Xpp using invF and X
Xpp = *******;
% Separate the x"(xpp) coordinates from the first row of Xpp
xpp = *******;
% Separate the y''(ypp) coordinates from the second row of Xpp
ypp = *******;


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% Plot a unit circle, the strain ellipse, and key eigenvectors in Fig. 1;
% a unit circle, the reciprocal strain ellipse, and key vectors in Fig. 2;
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% Plot the unit circle and strain ellipse; 
figure(1)
clf
plot(x,y,xp,yp)
% Set the axes of the plots to the same scale and title the plot usefully
axis equal
title('Unit Circle and Strain Ellipse')
% Now plot the key unit eigenvectors
hold on
plot([0,vF(1,1)],[0,vF(2,1)],'r',[0,vF(1,2)],[0,vF(2,2)],'r')
plot([0,vV(1,1)],[0,vV(2,1)],'b',[0,vV(1,2)],[0,vV(2,2)],'b')
hold off

% Plot the unit circle and reciprocal strain ellipse; 
figure(2)
clf
plot(x,y,xpp,ypp)
% Set the axes of the plots to the same scale and title the plot usefully
axis equal
title('Unit Circle and Reciprocal Strain Ellipse')
% Now plot the key unit eigenvectors
hold on
plot([0,vinvF(1,1)],[0,vinvF(2,1)],'r',[0,vinvF(1,2)],[0,vinvF(2,2)],'k')
plot([0,vU(1,1)],[0,vU(2,1)],'g',[0,vU(1,2)],[0,vU(2,2)],'g')
plot([0,vV(1,1)],[0,vV(2,1)],'b',[0,vV(1,2)],[0,vV(2,2)],'b')
% Now plot the retro-deformed principal strain axes
plot([0,Rps(1,1)],[0,Rps(2,1)],'c',[0,Rps(1,2)],[0,Rps(2,2)],'c')
hold off
