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Hi

I´m self-studying Alonso and Finn´s Mechanics and I have a question about this subject.

Let a body rotate about an arbitrary axis P having angular momentum [tex]\vec L [/tex].

Consider a referential with three perpendicular axes, [tex] X_{0} , Y_{0} , Z_{0} [/tex] , which are also principal axes of inertia.

The book says we can write [tex] \vec L [/tex] as

[tex] \vec L = \vec u_{x} I_1 \omega_{x0} + \vec u_{y} I_2 \omega_{y0} + \vec u_{z} I_3 \omega_{z0} [/tex]

Does anybody how to derive this formula? The book usually explains things, but perhaps this is supost to be obvious.

By the way, I already know how to derive [tex] \vec L = I \vec \omega [/tex] for a body rotating about a principal axis of inertia but I don´t know how to derive this one.

I´m self-studying Alonso and Finn´s Mechanics and I have a question about this subject.

Let a body rotate about an arbitrary axis P having angular momentum [tex]\vec L [/tex].

Consider a referential with three perpendicular axes, [tex] X_{0} , Y_{0} , Z_{0} [/tex] , which are also principal axes of inertia.

The book says we can write [tex] \vec L [/tex] as

[tex] \vec L = \vec u_{x} I_1 \omega_{x0} + \vec u_{y} I_2 \omega_{y0} + \vec u_{z} I_3 \omega_{z0} [/tex]

Does anybody how to derive this formula? The book usually explains things, but perhaps this is supost to be obvious.

By the way, I already know how to derive [tex] \vec L = I \vec \omega [/tex] for a body rotating about a principal axis of inertia but I don´t know how to derive this one.

Thank you

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