Kleppner & Kolenkow derivation error in free precession?

But in summary, the conversation discusses inconsistencies in the signs in equations 8.23, 8.24, 8.25, and 8.26 in the second edition of the book K&K. The speaker also mentions being unsure if they are missing something.
  • #1
natz
1
0
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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  • #2
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.
 

Related to Kleppner & Kolenkow derivation error in free precession?

1. What is the derivation error in free precession?

The derivation error in free precession refers to the difference between the theoretical equations for precession and the actual motion observed in a physical system. It is usually caused by simplifications or assumptions made in the derivation process.

2. How does the derivation error affect the accuracy of measurements?

The derivation error can affect the accuracy of measurements by introducing deviations from the expected behavior of the system. This can lead to discrepancies between predicted and observed values, making it difficult to make precise measurements.

3. What are some common sources of derivation error in free precession?

Some common sources of derivation error in free precession include neglecting frictional forces, assuming a perfectly spherical or symmetrical system, and ignoring the effects of external forces.

4. Can derivation errors be eliminated completely?

No, derivation errors cannot be completely eliminated as they are inherent in the simplifications and assumptions made in the derivation process. However, they can be minimized by considering more complex factors and refining the derivation equations.

5. How can we account for derivation errors in our experiments?

To account for derivation errors in experiments, it is important to carefully consider the assumptions and simplifications made in the derivation process and attempt to minimize their effects. Additionally, conducting multiple trials and comparing results can help identify any discrepancies caused by derivation errors.

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