# 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).

Step 1 of 6

Part (a)

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

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

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

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Textbook: Classical Mechanics

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