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What if jerk is the parameter to be held constant in a relativistic rocket?
Two versions of such a rocket: a simple flyby scenario, with beginning and ending accelerations specified, and a destination scenario, that will involve a flip turn at some point (but unlike the constant acceleration situation, not at halfway!). Initial velocities (and final for the destination scenario) should be zero.
I have just enough background physics to be interested in this, but my college courses never included the relativistic background to work it out easily for myself. I have a degree in maths so integrals etc. are fine, but space-time metrics may need some explaining if they come up.
A full-bodied relativistic rocket calculator offers distance, acceleration, max velocity (max lorentz factor), ship/earth times of journey, fuel/payload ratio. For constant jerk on a destination journey, I would also like to know when/where the flip would take place. I want to write such a calculator myself, I just need the equations, or a method of deriving them myself. (Of course I would not say no if someone pointed an existing one out to me.)
I also have the loftier goal of writing (or finding) a calculator that could give the above factors for any well-defined function of acceleration over time (or distance), if anyone knows of one or has been hoarding one on their hard drives.
[For the curious, there are various reasons why one might want to vary the initial and final accelerations that I can think of some offhand. For the flyby constant jerk rocket, it could set out to rendezvous with another ship having a different acceleration profile and wants its profile to smoothly match upon arrival, or it could depart with inhabitants temporarily acclimatized to one acceleration but with a preference for a "cruising acceleration" at a different level. For the destination constant jerk rocket, imagine flying from Earth to a Mars-gravity planet 10 light-years away, and having the entire flight as a slow adjustment period; alternatively, it seems to me that a constant acceleration rocket has to be working its engines a lot more in the beginning (when they have much more fuel mass to accelerate) than at the end; by keeping the engines on at full burn for constant thrust, acceleration will increase linearly throughout the flight.]