Coordinate System Transformations

In summary, the conversation discusses the coordinates of coordinate frames A and B, and how a rotation matrix can be calculated without knowledge of euler rotations. The suggested method is to look at how the standard basis vectors transform, as they are the columns of the rotation matrix. It is also noted that a rotation matrix may not always exist for a change of coordinate systems.
  • #1
phil0stine
5
0
Lets say I have Coordinate Frame's A and B.

and...

I have the coordinates of the 3 principle axes of B in terms of Frame A,

So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A:

XA -> -YB
YA -> XB
ZA -> ZB

My question is: Given a slightly more complex mapping, but without knowledge of euler rotations, how could a Rotation Matrix be calculated?

Thanks in advance
 
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  • #2
Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)
 
  • #3
JeSuisConf said:
Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)

Clean and simple, with the added bonus of triggering a very faint memory of learning that once.

Thanks so much for clearing it up, this is what I need for my application.
 

1. What is a coordinate system transformation?

A coordinate system transformation is a mathematical process used to convert coordinates from one reference system to another. This is often necessary when working with data or maps that use different coordinate systems.

2. What are some common types of coordinate systems?

Common types of coordinate systems include geographic coordinates (latitude and longitude), Cartesian coordinates (x and y), and polar coordinates (radius and angle).

3. Why are coordinate system transformations important in science?

Coordinate system transformations are important in science because they allow researchers to work with data from different sources and combine data from different coordinate systems. They also help to ensure accuracy and consistency in data analysis.

4. How are coordinate system transformations performed?

Coordinate system transformations are performed using a series of mathematical equations and algorithms. These calculations take into account the differences between the two coordinate systems, such as different units of measurement or different projections.

5. What are some challenges in performing coordinate system transformations?

Some challenges in performing coordinate system transformations include ensuring that the correct equations and parameters are used, dealing with complex or non-standard coordinate systems, and avoiding errors or distortions in the transformed data.

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