How is Work Calculated for a Constantly Accelerating Rocket?

[Nabeshin]

If I have a rocket constantly accelerating at some rate a, (requiring some constant force F), I want to know how much work is done by the rocket to travel a given proper length.

For example, a rocket traveling to alpha centauri at 1g acceleration half way and 1g acceleration the other half. It would seem work would just be F*d, however, the d should be as measured in the rocket's frame of reference. Would a correct method of deriving the d to be to take the velocity function of the rocket, integrate from 0 to some t (half way point), and then multiply by two (symmetry) to obtain total distance traveled in the frame of the rocket?

General note: the function I'm using for the time between two points also requires the measurement d. The equation is:
$$t=\frac{c}{a_0} Cosh^{-1}\left[1 + \frac{a_0 d}{c^2}\right]$$

with t being as measured on the ship. To get the time to the mid-way point (required for the above approach), is it valid to just set d/2? (and also multiply by two to get the entire shipboard time for the full voyage)

 

[stovepipe]

This might be helpful.

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

 

[Nabeshin]

Thanks for the link, that's actually where I got the posted time equation.

The only possibly applicable equation is that under the section "below the rocket ..." but I don't think that's quite it. That equation gives the remaining distance, or current distance at any time T, whereas I want the total distance traversed in the frame of the rocket... Unless I'm missing some basic calculus I can't get what I need from that equation.