Table Top Physics - Collision

Next consider a rigid body with most of its mass at 45 degrees to the y plane.

Ixx = sum (y^2)dm = 0.5+0.5 = 1

Iyy = sum(x^2) dm = 0.5+0.5 = 1

Ixy = sum(x*y)dm =0.5+0.5 = 1

det[M] = Ixx Iyy - Ixy Ixy = 0.25-0.25 =0

diagram

x/y = Ixy /(Ixx - lambda)

for lambda=0

x/y = 1/(1-0) = 1

normalising gives a unit vector at 45 degrees (along the line joining the masses).

for lambda=2

x/y = 1/(1-2) = -1

normalising gives a unit vector at -45 degrees (at 90 degrees to the line joining the masses)

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