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ohsoconfused

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## Homework Statement

Consider a thin homogeneous plate with principal momenta of inertia

I1 along axis x1,

I2>I1 along x2,

I3 = I1 + I2 along x3

Let the origins of the x and x' systems coincide at the center of mass of the plate. At time t=0, the plate is set rotatint in a force-free manner with angular velocity Q about an axis inclined at an angle of a from the plane of the plate and perpendicular to the x2-axis. If I1/I2 = cos2a, show at time t the angular velocity about the x2-axis is:

w2(t) = Qcosa*tanh(Qtsina).

## The Attempt at a Solution

I know that the kinetic energy and the square of the angular momentum are constant, but I'm not positive how to calculate them with the initial conditions given. Past that, the Euler equations simplify somewhat...

(for simplicity's sake, let [x] = the first time derivative of x)

[w2] = w3w1

[w1] = -w2w3

[w3] = w1w2*(I1-I2)/(I1+I2) = w1w2*(cos2a-1)/(cos2q+1)

I'm having trouble seeing how such a bizarre function can even arise, but I think my first problem is calculating KE and L squared in terms of the initial conditions, which I'm blank on.

Anybody help?