Function and change of frame of reference

In summary, the conversation discusses the consequences of changing the frame of reference on an ordinary function. It is mentioned that translations are possible, but rotations may cause the function to become multiple valued. It is also noted that while it is possible to express the function in terms of the new frame of reference, it may not be possible to solve for the new function explicitly.
  • #1
Konte
90
1
Hello everybody,

My question is about change of frame of reference and its consequences on an ordinary function.
Let's ##B## a frame of reference that is linked to another one ##B'## through a change of basis matrix ##M##.
So, for an equation written in the first basis ##B## as ##y=3x^2+2x-1##,
what will be the corresponding writing (let ##y'=...##) in the second basis ##B'## by the use of matrix ##M## ?

Thank you .

Konte.
 
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  • #2
The function defines a mapping from one variable to another. Changing those variables to another frame of reference will not normally retain a well defined function. Translations will be ok, but a rotation will often make the function become multiple valued.
 
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  • #3
You can always express y and x in terms of y' and x', but in general you cannot solve the resulting equation for y'. You can still get an implicit function.
 
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  • #4
Thank you guys for your answer.
 

1. What is a frame of reference?

A frame of reference is a set of axes or coordinates used to describe the position, orientation, and motion of an object in space. It is used as a point of reference to measure and understand the movement and changes of an object.

2. How does a frame of reference affect our perception of motion?

A frame of reference can greatly influence our perception of motion. For example, if we are in a moving car, our frame of reference is the car itself. This can make objects outside the car appear to be moving in the opposite direction, even though they are actually stationary. Our perception of motion is relative to our chosen frame of reference.

3. What is the difference between an inertial and non-inertial frame of reference?

An inertial frame of reference is one in which Newton's laws of motion are valid and objects move at a constant velocity unless acted upon by an external force. A non-inertial frame of reference is one in which Newton's laws do not hold true, typically due to acceleration or rotation.

4. How does the concept of relativity relate to frames of reference?

The concept of relativity states that physical laws and measurements are relative to the observer's frame of reference. This means that different observers may have different perceptions of the same event, depending on their chosen frame of reference.

5. Why is understanding frames of reference important in science?

Frames of reference are crucial in science because they allow us to accurately describe and predict the motion and changes of objects. By choosing a specific frame of reference, we can eliminate any potential confusion or discrepancies in our observations and measurements. This is essential for conducting accurate and reliable experiments and making scientific discoveries.

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