Kleppner & Kolenkow derivation error in free precession?

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SUMMARY

The discussion centers on potential errors in the derivation of torque-free precession presented in Kleppner & Kolenkow's second edition. The user identifies discrepancies in the signs of equations 8.25 and 8.26, suggesting that equation 8.25a should feature a negative cosine and 8.25b a positive sine. Additionally, the user questions the consistency of signs in equations 8.26a and 8.26b, proposing they should be opposite. This indicates a need for careful review of the equations to ensure accuracy in the derivation process.

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natz
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Hi all.
I ended up to this section in K&K (2nd edition, but with 1st is the same) when they derive the wobbling motion of a simple body in torque-free precession. [see the attached file]
Equations 8.23 and 8.24 are integrated into 8.25[a|b], but I think signs are wrong. Shouldn't be negative cosine in 8.25a and positive sine in 8.25b ?
Another problem is that equations 8.26[a|b] have the same sign, shouldn't they be opposite ?
This is the second edition of the book so I'm doubting if I'm tired and missing something.

Thanks in advance.
 

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There are obviously inconsistencies in this concerning the signs. Given (8.23) in the next line (un-numbered equation) the sign is already wrong, because
$$\dot{\omega}_x=+A\gamma \cos(\gamma t+\phi).$$
I don't have the book, so I can't check the context.
 

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