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How to trasform an orthonormal system in two reference frames

  1. Apr 26, 2012 #1
    My question is not homework. I feel ashamed of having this doubts but I'm really stuck on this.
    The problem is I have a reference frame xyz and here I define the COM [itex]\vec x{_{cm}}[/itex] of the system.
    Now I move the COM reference frame x'y'z':
    [itex]\vec{x'}=\vec{x}-\vec x{_{cm}}[/itex]

    In this reference frame I define a new orthonormal system x''y''z'' centered in (0,0,0), i.e. the COM mass.

    I now want to recover to component of my last orthonormal system x''y''z'' in the original system xyz.

    If I do:

    [itex]\vec{x''}{ {\rm (in~ xyz)}}=\vec{x''}{ {\rm (in~ x'y'z')}}+\vec x{_{cm}}[/itex]

    I don't recover an orthonormal system of axis! What is wrong in my method?
  2. jcsd
  3. Apr 26, 2012 #2


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    Science Advisor
    Homework Helper

    hi matteo86bo! :smile:

    i don't understand :confused:

    x' = x - xc.o.m

    so your xyz directions are the same, and only the origin has changed

    then x'' = x' + xc.o.m = x
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