The Cross Product in Non Orthogonal Coordinate Systems
The form of the cross product I’ve shown in my post Coriolis Forces is:
The components of this cross product can be written as follows:
We will abbreviate these relationships as follows:
Now define the coordinate transform:
where
Then the cross product components can be written as follows:
Now Right multiplying the matrix by the transform gives:
Which can be written in this form:
Where:

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