Partially rotated coordinate systems

In summary, a partially rotated coordinate system is a coordinate system where the axes are rotated at certain angles from their original positions. Scientists may use this type of coordinate system to simplify calculations, better represent certain physical phenomena, or when traditional Cartesian coordinates are not suitable. To convert between the two systems, rotation matrices or transformation equations can be used. The advantages of using a partially rotated coordinate system include simplifying calculations and more accurate results. However, there are limitations such as difficulty in visualization and the need for advanced mathematical knowledge. Additionally, it may not always be necessary or beneficial for certain applications.
  • #1
Bassalisk
947
2
Hello,

I am trying to understand this partially rotated coordinate systems.

I do not understand how does x'=xcos(theta)+ysin(theta) and y'=ycos(theta)-xsin(theta)

I am probably stuck at silly answer but i need this to understand deriving of formulas for special relativity.

Thanks
 

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Mathematics news on Phys.org

1. What is a partially rotated coordinate system?

A partially rotated coordinate system is a type of coordinate system in which the axes are not aligned with the traditional Cartesian axes. This means that the x, y, and z axes are rotated at certain angles from their original positions.

2. Why would a scientist use a partially rotated coordinate system?

Scientists may use a partially rotated coordinate system to simplify complex mathematical calculations or to better represent a specific physical phenomenon. It may also be used in situations where the traditional Cartesian coordinates are not suitable.

3. How do you convert between a partially rotated coordinate system and a traditional Cartesian coordinate system?

To convert between a partially rotated coordinate system and a traditional Cartesian coordinate system, you can use rotation matrices or transformation equations. These allow you to rotate the axes to the desired angles and then convert the coordinates accordingly.

4. What are the advantages of using a partially rotated coordinate system?

One advantage of using a partially rotated coordinate system is that it can simplify complex mathematical calculations, making them more manageable and easier to understand. It can also better represent certain physical phenomena, leading to more accurate results.

5. Are there any limitations or drawbacks to using a partially rotated coordinate system?

One limitation of using a partially rotated coordinate system is that it may be more difficult to visualize or understand compared to a traditional Cartesian coordinate system. It may also require more advanced mathematical knowledge to work with effectively. Additionally, using a partially rotated coordinate system may not always be necessary or beneficial for certain applications.

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