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

[MD LAT 1492]

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!

 

[anuttarasammyak]

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.

 

[MD LAT 1492]

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.

 

[anuttarasammyak]

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 ?

 

[MD LAT 1492]

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

 

[anuttarasammyak]

May I think You answer your question in OP as 2)?

 

[MD LAT 1492]

May I think You answer your question in OP as 2)?

Ok now I also think that is the answer. Thank you