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Consider the rapid steady precession of a symmetric top
Chapter 10, Problem 10.52(choose chapter or problem)
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
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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).
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
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