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Coordinate Transformation - velocity?

  1. Mar 12, 2009 #1
    If I have a velocity vector V in some coordinate system. Is there anything special that needs to be done to convert V -> V' ?

    Basically, I have a matrix (N x 3) in north-east-down coordinates. I am trying to convert (a row at a time_ to another matrix (N x 3) to earth-centered-earth-fixed coordinates.

    When I do the transformations with positions, it seems okay. When I do the transformation with velocity "positions" it seems messed up?


    Any ideas?
     
  2. jcsd
  3. Mar 13, 2009 #2
    From,
    http://en.wikipedia.org/wiki/Geodetic_system

    The transformation matrix from ENU-coordinates to ECEF is:
    16a633282014bfdae7efd24bfa65d47d.png
    Figure 1 - Transformation Matrix


    Working with this, I have found that when (x,y,z) and (Xr, Yr, Zr) represent positions vectors, the transformation works fine.

    However, when (x,y,z) and (Xr, Yr, Zr) are velocity vectors... actually, I think I just answered my own question.

    I only have (Xr, Yr, Zr) as a position-vector. And (x,y,z) as a velocity-vector.


    Okay... how about this? In general terms, does Figure 1 - Transformation Matrix work for transforming velocity vectors?
     
  4. Mar 14, 2009 #3
    There are transformation laws for a vector of rank-one either covariant or contravariant. Velocity is a vector quantity. it must obey a transformation law. For more detail check the book: Tensor Analysis by Sokonikoff
     
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