I'm working on a sci-fi story with a few locations set across the solar system, and I want to make sure that it works as accurately as possible. In order to hop from planet to planet, the ships use energy beamed from a network of satellites across the system to continuously push them; cutting travel times down to only days or weeks per trip, removing the need for the ship to carry fuel mass, and generating artificial gravity on board in the process.
However, rather than just simply burning at a constant rate, I want the acceleration of the drives to rise and fall throughout the duration of the flight so passengers could adapt to the change in gravity when arriving at another planet. For example, a ship leaving Earth would start its transfer at 9.8 m/s of acceleration, but over the course of a few days the satellites would "throttle down" the force applied on the ship so that by the time it arrived at Mars, it would only accelerating at 3.7 m/s.
Also, somewhere in the middle of the flight there would have to be a point where the ship would have to stop its thrust, take 20 seconds to turn around, and continue thrusting in reverse in order to slow down. But even with this direction change, I want it to stop and resume it's change in acceleration like nothing happened (it would account for the gap in between, but it wouldn't need to alter the rate of change of acceleration afterwards).
Can someone please show me how I can calculate such a flightpath?