First consider a rigid body with most of its mass at +1 and -1 on the y plane.
Ixx = sum (y^2)dm = 1+1=2
Iyy = sum(x^2) dm = 0
Ixy = sum(x*y)dm =0
det[M] = Ixx Iyy - Ixy Ixy = 0-0 =0
(Ixx - )*x = Ixy *
y
x/y = Ixy /(Ixx - )
for =0
x/y = 0/2=0
normalising gives a unit vector in the x direction {1,0}T
for =2
x/y = 0/0=?
using the bottom equation
(Iyy - )*y = Ixy *
x
y/x = Ixy/(Iyy - )
for =0
y/x = 0/0 = 0
for =2
y/x = 0/(0-2)=-0.5
normalising gives a unit vector in the y direction {0,1}T
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