Relativistic Frictional Force

[camacazio]

After some simple frictional mechanics work, and some fancy derivative work with relativistic values, I got a value for the rate of change of expansion for the rocket ship on the frictional surface:

v = initial velocity
n=coefficient of static friction
g=gravitational accelleration on earth=9.8m/s^2
L=proper length of the rocket ship sliding on the high friction surface in meters
c=speed of light in a vacuum
t=time in seconds

accelleration of expansion = (-1/2)(ng)^2*L/(1-[(v-ngt)/c]^2)^(3/2)

However, that accelleration seems faulty. All my other values seem correct, but this one doesn't look so good. It has no initial value to reduce from, so this implies that the accelleration will go to (-1/2)(ng)^2*L as t goes to infinite. It should, of course, go to 0 as t goes to infinite, because the ship will reach it's proper length and then stop having any change in length.