Torque-free precession and angular momentum in rotating frames

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nonequilibrium
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Hello, I quote http://en.wikipedia.org/wiki/Precession from the first paragraph from the first section ("Torque-free precession"):

For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. This occurs because the angular momentum (L) is constant in absence of torques. Therefore it will have to be constant in the external reference frame, but the moment of inertia tensor (I) is non-constant in this frame because of the lack of symmetry. Therefore the spin angular velocity vector (ωs) about the spin axis will have to evolve in time so that the matrix product L = Iωs remains constant.

But isn't the matrix product L = Iωs relative to the moving frame (that's how we did it in our course anyway), meaning L and omega are indeed the vectors as defined/seen from the absolute/fixed frame, but the matrix product has the components from the moving/relative frame. In that case, those components of L don't have to be fixed, since a fixed L in the absolute frame will seem to be rotating/changing when seen from the moving frame.
 

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hello mr. vodka! :smile:
mr. vodka said:
But isn't the matrix product L = Iωs relative to the moving frame (that's how we did it in our course anyway), meaning L and omega are indeed the vectors as defined/seen from the absolute/fixed frame, but the matrix product has the components from the moving/relative frame. In that case, those components of L don't have to be fixed, since a fixed L in the absolute frame will seem to be rotating/changing when seen from the moving frame.

the angular momentum (I) is best defined in the moving frame (the frame fixed in the body and rotating with it) because it's fixed in the structure, and in a stationary frame it would be changing

but you can define the angular momentum in the stationary frame, which is what wikipedia is doing to make it clear that a constant Iω and a changing I means a changing ω

we can work in either frame …

if all we want to show is that ω must be changing, then the stationary frame is easiest, but if we want to actually find the equation for ω, it's best to use the moving frame and Euler's equations :wink:
 
Aha, that makes a lot of sense, thank you! :)