There is an idea for (soft) sf strategy game following me for a long time but I need to get a grasp of some math before moving further with it.
Lets assume there is a spaceship traveling (in space) with some velocity and its engines can generate some acceleration - with maximum acceleration much smaller in magnitude than obtainable velocity. Now given the planned use of engine (acceleration in time) I think ti is fairly straightforward to calculate movement of the ship.
But the problem I need to solve is reverse - given starting position, velocity and desired destination I need to find a plan of engine usage (acceleration over time) that will guide the ship to the destination in minimal time.
There may be some complications like
- The ship can only accelerate in one direction and turning (changing direction) takes time
- There are some large bodies with gravitational pull that affects ship course
- The destination point is moving in time - for example it is relative to planet or moon orbiting larger body
- The timing is important - for example the ship is flying in fleet and need to arrive on target at roughly same time as her companions
Now I do not expect to get ready to use solution but my question is where I could look for clues? What I should study? What similar problems or related algorithms can help?
As this is for a game the solution may be simplified and even involve some "cheating" that would not work in real life.