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Euler equations in rigid body: Taylor VS Kleppner - Kolenkow

  1. Jun 25, 2015 #1
    Hello all.

    After reading both chapters on rigid body motion both in Kleppner - Kolenkow and Taylor books, I still do not undertand the physical meaning of Euler equations. Let me explain:

    In Kleppner - Kolenkow, they claim (page 321 - 322) that in Euler equations, Γ1, Γ2 and Γ3 are the components of the torque as viewed in the inertial (space) frame at some time t, ω1, ω2, ω3 are the components of angular velocity in that same frame, and dω1/dt, dω2/dt, dω3/dt the instantaneous rate of change of those components. Thus, Euler equations relate all these quantities in the inertial space frame at time t.

    On the other hand, in page 396, Taylor says that the Euler equations determine the motion of a spinning body as seen in a frame fixed in the body (so I guess he means, as seen in the body frame). So Γ1, Γ2 and Γ3, and ω1, ω2, ω3, are the componnetes of torque and angular velocity in the rotating body frame.

    As you see, I am really confused. Besides, to derive Euler equations, Kleppner - Kolenkow use a vector approach and the small angle approximation, while Taylor uses a relation between inertial and non inertial frames, which I have nor studied yet, and maybe this is the source of my confusion.

    Are they the same statement, but explained in diffrents ways? If so, I do not understand it.

    Is any of the explanations wrong? If so, which is the correct one?

    Thanks a lot for your help.
     
    Last edited: Jun 25, 2015
  2. jcsd
  3. Jun 25, 2015 #2
    Hi
    I'm not sure, but i guess they mean the inertial frame of referece. If they meant frame of the body, ω would be zero as well as ∝. But you should wait for an answer of someone more experienced :)
     
  4. Jul 14, 2015 #3

    vanhees71

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    The Euler equations are in the non-inertial frame comoving with the top (body frame).
     
  5. Jul 15, 2015 #4
    Thanks for your reply. That is what I thought, too.

    Then, there must be a mistake in Kleppner - Kolenkow's book (or, at least, they do not explain it properly, because that is what I understood after reading that section).
     
  6. Jul 15, 2015 #5

    vanhees71

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