# Table Top Physics - two masses

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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