Relativistic integration

Hi All,

I have written a program to integrate motion paths of charged
relativistic particles in a stationary electric field, and I have run
into a (rather serious) problem.

All coordinates are cartesian vectors (x,y,z).
r(t) is the position of the particle at the time t,
v(t) is the velocity,
a(t) is the acceleration and
dt is the step time.

I the integration method called velocity verlet. It looks like this:

(1) r(t+dt) = r(t) + v(t)*dt + 1/2 * a(t)*dt^2

(2) v(t + dt/2) = v(t) + 1/2 * a(t)*dt

(3) v(t + dt) = v(t + dt/2) + 1/2 * a(t + dt)*dt

I already know the acceleration from a NASA report by Charles Buhler et al.

(
The report can be found at
http://www.niac.usra.edu/files/studi.../921Buhler.pdf
)

Now my question is this: How do I transform the velocity verlet
algorithm above into a relativistic equivalent?

I suppose I need to divide dt by gamma, and use relativistic velocity
addition to calculate the velocities in (2) and (3), but I am somewhat
uncertain as to how this is done (what the equations look like), and
also if it is correct.

Any help would be appreciated.

Kind regards

- Frank Sorensen

Le vendredi 29 juillet 2005 12:49:14 UTC+2, Frank Sorensen a écrit*:
Now my question is this: How do I transform the velocity verlet
algorithm above into a relativistic equivalent?

I suppose I need to divide dt by gamma, and use relativistic velocity
addition to calculate the velocities in (2) and (3), but I am somewhat
uncertain as to how this is done (what the equations look like), and
also if it is correct.

Any help would be appreciated.


Hello! I'm interested to this answer two! Do you have any further
elements since this post?

Kind regards,
Mathieu

[Mod. note: quoted text trimmed -- mjh]