Relative Motion & Local Frame’s Position - when projecting components

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Discussion Overview

The discussion revolves around the concept of relative motion and the positioning of coordinate frames in relation to a rotating body. Participants explore whether the origin of a rotating coordinate frame should be fixed to the moving body or to an inertial frame, while also considering the implications of these choices on the description of motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the origin of the rotating coordinate frame should be fixed to the moving body or to an inertial frame, emphasizing the need for clarity in the definition of the frame's position.
  • Another participant suggests that the discussion is more mathematical than physical, indicating that the laws of physics in a rotating frame can be complex.
  • A participant describes a specific scenario involving spherical motion, noting confusion about the position of the spherical coordinate frame's origin relative to an inertial frame.
  • Some participants agree that the center of spherical motion and the coordinate axes should remain at rest in an inertial frame, allowing for freedom in angular coordinates.
  • There is a suggestion that the original poster's question aligns with the idea of fixing the origin to the inertial frame, which is later affirmed by the original poster.

Areas of Agreement / Disagreement

While some participants express agreement on certain aspects of the discussion, such as the positioning of the coordinate frame's origin, there remains uncertainty regarding the implications of these choices and the complexity of the laws governing motion in rotating frames. No consensus is reached on the broader implications of the initial question.

Contextual Notes

The discussion includes assumptions about the nature of the motion and the definitions of the coordinate frames, which may not be fully articulated. The complexity of the laws of physics in rotating frames is acknowledged but not resolved.

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Does the position of the origin for the body’s rotating coordinate frame
1) stay fixed to the moving body or
2) does it stay fixed to the inertial frame, yet still able to rotate as the body rotates with the only restriction that it cannot translate with the body i.e. only affixed at the inertial frame.

thank you and I appreciate the time you take to answer this!
 
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As you wish. For an example, say the body is at rest in inertial frame of reference. You can set any frame of reference where the body is rotating ( not the body but you spin. ) and the Origin moves or fixed as you wish to set. This is rather mathematics discussion than physics. The law of physics in that frame is very messy one.

I think you have more specific case in mind saying "the body is rotating". I would like to know it.
 
Last edited:
anuttarasammyak said:
As you wish. For an example, say the body is at rest in inertial frame of reference. You can set any frame of reference where the body is rotating ( not the body but you spin. ) and the Origin moves or fixed as you wish to set. This is rather mathematics discussion than physics. The law of physics in that frame is very messy one.

I think you have more specific case in mind saying "the body is rotating". I would like to know it.
Thank you for your answer and it has helped remind me.

In my problem, I was describing the spherical motion of a body (a) relative to an inertial frame (o), where I had placed the spherical unit vectors and also that spherical coordinate frame's origin at the body - this is the part that confused me.

Because when I described the position vector of (a) relative to inertial origin (o) in terms of the spherical basis, it showed that my position was in the negative radial direction.

I know that by just multiplying by a negative would flip the direction, but this brought up the question of where the generated spherical origin is actually positioned.

In my mind, I can only think that the generated spherical coordinate frame's origin should be positioned at the origin (o) to make sense.
 
From what you said I assume the case you set is :
The center of spherical motion O and OXYZ axes stay at rest in a IFR
r, the distance from the center O, remains constant. So the motion has freedom of ##\theta## and ##\phi##.
Is it all right ?
 
Last edited:
anuttarasammyak said:
From what you said I assume the case you set is :
The center of spherical motion O and OXYZ axes stay at rest in a IFR
r, the distance from the center O, remains constant. So the motion has freedom of ##\theta## and ##\phi##.
Is it all right ?
Yes
 
May I think You answer your question in OP as 2)?
 
Last edited:
anuttarasammyak said:
May I think You answer your question in OP as 2)?
Ok now I also think that is the answer. Thank you
 
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