Solution Found!

Consider the rapid steady precession of a symmetric top

Chapter 10, Problem 10.52

(choose chapter or problem)

Get Unlimited Answers
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,

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

Add to cart

Reviews

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

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Classical Mechanics

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back