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I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis.

I've seen the following approach which I don't understand:

One contribution to change in ##L_z## is due to rotation about y axis. This causes ##L_x## to rotate and hence a component ##-L_x \Delta{_y}## appears.

How do we know that ##Lx## will remain constant in magnitude? Also the actual motion won't be as is shown, in which the body simply goes around the y-axis while maintaining it's spin ##L_x##

A similar method is used here by

*Kleppner and Kolenkow*here

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