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Find a vector to a particle from a rotated reference frame

  1. Aug 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a particle in space whose position vector from the origin of reference frame i is
    given by the expression r(Oi to P) = 37t(Ii + Ji + Ki). The distance vector from the origin of
    another reference frame (m) to the origin of the I reference frame is given by
    r(Om to Oi) = e^(-2t)Ii. The i and m frames are initially aligned at time equal zero, but over time the m reference frame wobbles or oscillates about the Ki axis. The rotation angle (θ) between the two reference frames oscillates according to θ = sin(13t). Determine the distance vector to the particle from an observer on reference frame m.


    2. Relevant equations

    No equations really....getting the correct components is what I'm after.


    3. The attempt at a solution

    I first setup reference frame i and placed point P somewhere in positive Ii, Ji, Ki space. Next, I drew another reference frame (m), such that Im and Ii are in the same line of action. All other planes are parallel. I went ahead and put the distance vector r(Om to Oi) on the Im axis (directionally equivalent to the Ii axis). Then, I drew the m reference frame again. This time rotated by some arbitrary angle to get an idea of what it looks like. From the origin in m, I drew a line to P. Now, I need to find the Im, Jm, and Km components. I know that part of my Im component will have the magnitude of e^(-2t) included. For this component I think the full term would be (e^(-2t) + 37tcos(sin(13t))Im. My other thought is because I can use the "tip to tail" method with vectors, all I need to show is (e^(-2t)Im + 37t(Ii)). However, now I don't know how to translate Ii to the Im reference frame. Then, I just don't know what to do to try and determine the Jm and Km components to P. I'm not very good at visualizing 3D space. Any help would be appreciated!
    Thank you
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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