Lesson 41
Non-Laminar Rotations and Stability of Rotations of a Rigid Body

Name:faculty Section:M2 Start Time:15:29:18 Instructor:pate Course:355

1) What does it mean for a rotating rigid body to be rotating stably? What about unstably? How do these kinds of rotations actually look? And how are they characterized mathematically?



2) See if you can find a rubberband or a piece of string, and use it to hold the covers of your textbook closed. By tossing your book into the air with an angular velocity about each of its three different principal axes (one at a time!), determine which moment of inertia is the greatest, which is the least, and which is the intermediate value. Please explain how you determine the relative sizes of the moments of inertia.

(See? You really can use your textbook for something useful! :-))



3) The Euler's equations for a rigid body

  1. each equal zero when the object moves under the influence of no force.
  2. describe how the components of the body's rotation rate change in time.
  3. show that an applied torque changes the angular momentum of the body, which in turn causes the rotation to change.
  4. are derived from the Lagrangian of the rotating object.
  5. more than one of the above.



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