# Coordinate Transformation - velocity?

1. Mar 12, 2009

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. Mar 13, 2009

From,
http://en.wikipedia.org/wiki/Geodetic_system

The transformation matrix from ENU-coordinates to ECEF is:

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?

3. Mar 14, 2009

### de_brook

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