- #1

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- Summary:
- How is the this normally handled?

Let's same I have an observer A and B that initially occupy the same point at ##t=0## but they have a relative velocity to each other.

Now let's assume there is an object C that moves in a circular motion around some point from A's frame. The initial condition/position is given (in A's frame).

What is the usual procedure to transform C into B's frame? Given that the SoS (surface of simultaneity) disagrees between A and B it seems to be quite a complicated task. My guess would be that the most general approach would be to calculate the entire trajectory of C, which in this case should form a helix in A's spacetime and then calculate the SoS of B and determine where they intersect. That would be where C is located at ##t=0## in B's frame, right?

I guess for objects moving with constant velocities and some other special cases there are formulas to simplify the calculation. But for a non-trivial movement this seems to be quite a lot of work. It's also quite annoying for the idea of an initial conditions which therefore are frame specific, i.e. not so "initial" from the perspective of other frame.

Now let's assume there is an object C that moves in a circular motion around some point from A's frame. The initial condition/position is given (in A's frame).

What is the usual procedure to transform C into B's frame? Given that the SoS (surface of simultaneity) disagrees between A and B it seems to be quite a complicated task. My guess would be that the most general approach would be to calculate the entire trajectory of C, which in this case should form a helix in A's spacetime and then calculate the SoS of B and determine where they intersect. That would be where C is located at ##t=0## in B's frame, right?

I guess for objects moving with constant velocities and some other special cases there are formulas to simplify the calculation. But for a non-trivial movement this seems to be quite a lot of work. It's also quite annoying for the idea of an initial conditions which therefore are frame specific, i.e. not so "initial" from the perspective of other frame.