Well, I wasn’t really aiming at the twin paradox aspect itself, but more at working out the calculation from the perspective of a rotating frame, which I hadn’t done before.
Your explanation of the constant ratio is very clear, thanks!
As for the circular motion, whether you imagine thrusters...
Yeah, definitely! You also have "math" "\math" tags, but such forums/platforms usually have a button to put them there. (Isn't there such a button here on PhysicsForums?)
But I don't really understand.
I see your point about dimensions, but from the standard derivation in polar coordinates the cross term really does come out with ##2 \omega r^2##.
Starting with flat spacetime in polar coordinates,
$$ds^2 = -c^2 dt^2 + dr^2 + r^2 d\theta^2,$$
$$ds^2 = -c^2...
Thanks for the replies and sorry I didn't reply earlier. (I was a bit sick and got really sick after posting this question, feeling a bit better right now.)
I'm afraid that if I post what I did exactly, it will be quite confusing, since it was an awnser to a pretty weird "Circular Twin/Triplet...
So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right.
Couls someone point me in the right direction?
"What have you tried?"
Well, trying to help truly...