Precession - why decompose to angular momentum component?

Question

I always see it is conventional (in Landau-Lifshitz for example) to decompose the angular velocity vector to 2 components: axis of symmetry and angular momentum vector, and then define the angular momentum part as $Omega_p$, meaning the precession component. My question is, why? Why not orthogonal components? Why is the angular momentum component considered the precession component? Is it a mere definition?

R.W. Bird · Answer

The direction of change for the angular momentum vector follows a circle which lies in a plane defined by the torque vector and its rate of change. Calculations for that circular motion are most easily handled by using a component of the angular momentum which lies in that plane.

Answered by R.W. Bird on July 8, 2021

Precession - why decompose to angular momentum component?

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