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Dr/Dt world coordinates problem

  1. May 16, 2007 #1
    1. The problem statement, all variables and given/known data
    In rigid body, r is the position of a rigid body relative to world coordinates,
    dr/dt is the rate of change of r in world coordinates.
    I encountered the term Dr/Dt as the rate of change of r in world coordinates relative to the body coordinates system.
    And that Dr/Dt = dr/dt-wxr
    My question is, how does Dr/Dt is called? (terminology)
    Also the operator D/Dt has the same rules as the operator d/dt, how do you proove it? There is some relationship to proove this, but what is this relation ship?

    2. Relevant equations
    Dr/Dt = dr/dt-wxr

    3. The attempt at a solution
    I tried to use Dr/Dt = dr/dt-wxr to proove that both operators has the same rules, but didnt succed.
    In matter of fact, I found some contradiction.
    For instance: d(AxB)/dt = Ax(dB/dt)+(dA/dt)xB
    So D(AxB)/Dt = Ax(DB/Dt)+(DA/Dt)xB should also be true.
    However using Dr/Dt = dr/dt-wxr showed that there is inequality.

    Thank you.
  2. jcsd
  3. May 16, 2007 #2
    I prefer the notation


    where r^s = space fixed r (with subscript s) and r^b = body fixed r

    The d/dt operator is the same in both cases.

    There's a good, but lengthy article here

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