Relativistic Circular Motion: Lorentz Boosting Among Accelerating Frames

[quantumdude]

I am working on a problem, and have gotten stuck.

Two masses orbit around a stationary attracting center with radii R₁ and R₂, R₁<R₂. They orbit in such a way that, in frame S₁, the Sun, S₁, and S₂ are all collinear.

I am using Marzke-Wheeler coordinates for accelerated observers, detailed here:
http://xxx.lanl.gov/pdf/gr-qc/0006095

The scenario for a single frame in circular motion is described on page 19.

What I want to know is, what do I have to do to Lorentz boost among accelerating frames? Is it the old LT, or do I have to modify it for the acceleration?

Thanks,

 

[dock]

Tom!

i don't know what you're going to think of me but i can simulate gravitational or Coulombian rotations without acceleration in the calculus.would it be of any help?

 

[quantumdude]

How do you simulate circular motion without rotations? Remember, this is not general relativity. Also, do you know how to address the question at hand, namely: Is there anything special I need to do to Lorentz transform between accelerated frames?

 

[dock]

Originally posted by Tom
How do you simulate circular motion without rotations? Remember, this is not general relativity. Also, do you know how to address the question at hand, namely: Is there anything special I need to do to Lorentz transform between accelerated frames?

no.i didn't meant circular motion without rotations (it's impossible)but "simulating circular motion without acceleration in the calculus of the trajectories".i'm so anccious to start working on that simulation in delphi.i don't have the language at the moment.i'll start tommorow.i can give you a clue of what I'm thinking by writing it down in MSWord and mail it to you.by the way you could be the first to (dis)agree with it.

regarding your q since there is no need of acceleration in the calculus you don't need to do any changes to LT.just use them how they are.at least this is how i understand your q;as if you wonder wather you need to acomodate LT to support transpassing between accelerated frames.

 

[quantumdude]

Originally posted by Tom
How do you simulate circular motion without rotations?

Sorry, I meant "acceleration", not "rotations". You can do this in GR, because an orbit is a free-fall frame, but in SR it is still considered an acceleration.

 

[dock]

i'll post what i have on it in the attachment.It's only classical physics but not usual classical physics but classical physics in marsian sense.

Don't forget to tell me about your inpresions!

 

[Janus]

Tom, maybe this will help:

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

 

[DavidW]

accelerated transformations

I think that the paper made a mess of something fairly simple. The transformations that they gave and which the paper are all about ARE the Lorentz transformations modified to describe particular states of acceleration. 1 constant proper acceleration and 2 circular motion. They are Lorentz boosts. I have transformation for arbitrarily accelerated states.
see equation 5.4.4 at-
http://www.geocities.com/zcphysicsms/chap5.htm#BM5_4
These are a Lorentz boost from an arbitrarily accelerated frame including orbital motion without "spin" to an inertial frame. At the following link there is an example on their use which is applied to an accelerated observer who orbits a center that is taken as the origin for an inertial frame. Relating two arbitrarily accelerated frame coordinate systems would be done in general by first relating each to a common inertial frame through equations 5.4.4 and then solving the systems of equations simply by first setting the right hand side of each system equal to each-other.

 

[dock]

Tom!

please check this thread:
https://www.physicsforums.com/showthread.php?s=&threadid=912

find the post with the algoritam for the simulation.

 

[schwarzchildradius]

Whatever the source of the potential

&gamma; = (1-(dU/drc²)^-1/2

learned that one from Creator.