Switching between frames of reference

[csocean]

hey :)

So, I'm trying to switch between from one frame of reference to another, for a rotation of a 3d object. First of all, the object is rotated, through 2 perpendicular axis. Now, I need to model that rotation in another set of predefined Euler rotations.

In other words, imagine a clock - the hands rotate to a particular time, then the clock itself is rotated through and axis that passes through 12 and 6 o'clock. I need to then express that orientation in predefined rotations, that pass through 12 and 6, followed by an axis through the face of the clock, then through the 12 and 6 again (bearing in mind that the clock face has moved, thus the 12 and 6 axis has been moved from it's previous position.)

I'm really struggling to grasp the geometry here! Any discussion that might give me a grasp of how to think about it (physically or mathematically!) would be most helpful!

 

[jimvoit]

Need Problem Clarification

I don't quite understand the problem. Here’s the difficulty:

Suppose we represent the clock in a 3D Cartesian coordinate system in which the x-axis comes out of the face towards the observer, the y-axis is at 3 , and the z axis is at 12. The first rotation you describe is about x, the second is about z for an Euler sequence of x z.

You then wish to replace this sequence by the sequence z x z. This can be accomplished by a first rotation about z of 0 degrees. I don’t think this is what you had in mind.

 

[astrokreng]

I understand your struggle with switching between frames of reference. This is a common challenge in many fields of science, including physics and mathematics. In order to fully grasp the concept, it may be helpful to first understand the concept of frames of reference.

A frame of reference is a coordinate system that is used to describe the position and motion of objects. It is essentially a way to measure and track the movement of objects in space. In your example, the clock serves as a frame of reference for the hands as they rotate.

When switching between frames of reference, it is important to consider the relative position and orientation of the two frames. In your case, the first frame of reference is the original orientation of the object, while the second frame of reference is the new set of predefined rotations.

In order to express the rotation in the second frame of reference, you will need to use a mathematical transformation known as a rotation matrix. This matrix allows you to convert the coordinates and orientation of the object from one frame of reference to another.

To fully understand the geometry of this process, it may be helpful to visualize the rotations in three-dimensional space. You can also think about it in terms of how the object moves and its position relative to the two frames of reference.

I hope this helps give you a better understanding of switching between frames of reference. It can be a complex concept, but with practice and visualization, you will be able to master it. Keep exploring and don't hesitate to reach out for further clarification. Good luck!