Handling Rotational Degrees of Freedom in Coordinate Transformations

In summary, the conversation discusses the challenges of analyzing the response of a dynamic system using different coordinate systems. The source disturbance is described as being about x, y, theta, and phi, and the goal is to obtain the response in a different coordinate system that is inclined to the initial one. While it is relatively easy to transform x and y using a transformation matrix, the transformation of rotational degrees of freedom is more complex. The speaker shares their attempt at using spherical and cartesian coordinates, but finds the process too tedious. They ask if there is a better alternative, but it seems that there is no easier way and that consolidating transformation matrices may be the best approach. The potential issue of "gimbol lock" and the use of qu
  • #1
chinmay
6
0
I am trying to analyse response of a dynamic system. The source disturbance is about x,y,theta (rotation about x ) & Phi of one coordinate system (red coloured coordinate system in the attached figure).

I need to get the response in another coordinate system ( green coloured coordinate system in the attached figure), whose all three axis is inclined to initial coordinate system.

In case of only x & y,it can be easily done using transformation matrix, but how to handle the transformation of rotational dof.

I tried to convert the source disturbance in spherical coordinate system , then cartesian, then transformation and finally again to (X, Y, Z, THETA, PHI, PSI,) new coordinate system; but this process is to tedious.

Is there any better alternative is available ?
Picture1.png
 
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  • #2
There is probably no easier way. If some of the transformations are constant, they can probably be combined into a consolidated transformation matrix. When using phi, psi, theta Euler angles, you need to be careful about "gimbol lock", where the angles are not well defined and it is hard to represent motion continuously. That can force you to use quaternions, which is a can of worms. Hopefully, you will not need to use quaternions.
 

Related to Handling Rotational Degrees of Freedom in Coordinate Transformations

1. What is meant by "coordinate transformation"?

Coordinate transformation is the process of converting coordinates from one coordinate system to another. This is commonly used in mathematics, physics, and geography to simplify calculations or to describe the same location using different systems.

2. Why is coordinate transformation important in scientific research?

Coordinate transformation is important in scientific research because it allows for easier and more accurate analysis of data. By converting coordinates to a common system, scientists can compare and combine data from different sources. It also allows for the use of different coordinate systems for different purposes, depending on the specific needs of the research.

3. What are the different types of coordinate systems used in coordinate transformation?

The most common types of coordinate systems used in coordinate transformation include Cartesian coordinates, polar coordinates, geographic coordinates (latitude and longitude), and projected coordinates (UTM, State Plane, etc.). Each system has its own advantages and is used for different purposes.

4. How is coordinate transformation performed?

Coordinate transformation is usually performed through mathematical equations or algorithms that convert coordinates from one system to another. These transformations can be simple, such as converting between Cartesian and polar coordinates, or more complex, involving multiple steps and calculations.

5. Are there any challenges or limitations in coordinate transformation?

There can be challenges and limitations in coordinate transformation, depending on the complexity of the transformation and the accuracy of the data. In some cases, there may be errors or discrepancies in the data that can affect the accuracy of the transformation. Additionally, some coordinate systems may not be compatible or may require additional information for a successful transformation.

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