### Solution Found!

# Consider the rapid steady precession of a symmetric top

**Chapter 10, Problem 10.52**

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**QUESTION:**

Consider the rapid steady precession of a symmetric top predicted in connection with (10.112).

(a) Show that in this motion the angular momentum **L** must be very close to the vertical. [Hint: Use (10.100) to write down the horizontal component \(L_{\text {hor }}\) of **L**. Show that if \(\dot{\phi}\) is given by the right side of (10.112), \(L_{\text {hor }}\) is exactly zero].

(b) Use this result to show that the rate of precession \(\Omega\) given in (10.112) agrees with the free precession rate \(\Omega_{\mathrm{s}}\) found in (10.96).

### Questions & Answers

(1 Reviews)

**QUESTION:**

Consider the rapid steady precession of a symmetric top predicted in connection with (10.112).

(a) Show that in this motion the angular momentum **L** must be very close to the vertical. [Hint: Use (10.100) to write down the horizontal component \(L_{\text {hor }}\) of **L**. Show that if \(\dot{\phi}\) is given by the right side of (10.112), \(L_{\text {hor }}\) is exactly zero].

(b) Use this result to show that the rate of precession \(\Omega\) given in (10.112) agrees with the free precession rate \(\Omega_{\mathrm{s}}\) found in (10.96).

**ANSWER:**

Step 1 of 6

Part (a)

With the help of the equation (10.100), the expression can be written as,

\(L=\left(-\lambda_{1} \dot{\phi} \sin \theta\right) \mathbf{e}_{1}^{\prime}+\lambda_{1} \dot{\theta} \mathbf{e}_{2}^{\prime}+\lambda_{3}(\dot{\psi}+\dot{\phi} \cos \theta) e_{3}\)

### Reviews

### Review this written solution for 103818) viewed: 694 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 10 - Problem 10.52

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