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Accelerated reference frames equation derivation question

  1. Feb 26, 2013 #1
    my question comes from the portion of the derivation regarding evaluating the rate of change of the principle axis vectors. this begins by supposing a vector, Q, is rotating about axis n by δθ. Specifically, my question is how from step 4 to step 5 the approximation becomes an equality.

    Q' can be approximated as:
    1. Q' ≈ Q + (|Q|sinα)δθ(in direction of n cross Q)
    2. Q' ≈ Q + |n cross Q|(in direction of n cross Q)δθ
    3. Q' ≈ Q + (n cross Q)δθ
    4. Q' ≈ Q + δθ cross Q

    The derivation then states: "This means that we can express the derivative of this vector as:
    5. (Q'-Q)/dt = (δθ cross Q)/dt
    6. dQ/dt = δθ/dt cross Q
    7. dQ/dt = Ω cross Q
     
  2. jcsd
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