I am writing physics engine in C++ and I am stuck on advanced math problem.
I need equation that allows me update the position of a moving point in 1-D expanding and accelerating space.
Just good old number on x-axis, that is interpreted as position of the point, relative to 0 (beginning). //any non-expanding units will work
Now the trick, is that the point is moving and the space (1D-line) is continuously being stretched. The expansion is completely smooth - not quantized (but I think we can use quantized version of this problem and using limit or other tool, converge on the continuous solution.
The input for the equation are these variables: velocity of the point, velocity of the initial expansion, acceleration of the expansion.
Output is just position of the point on the X axis.
//small suggestion on the solution
Lets make our units for this problem, imagine point 2. on same x-axis that is also moving, but doesnt experience the expansion of space (just for the sake of argument). We can set the distance of point 2. as 1 for making custom unit and refrence the expanding point 1 position as multiple of distance of point 2 from the beginning (still no stretching happens in points 2 frame of refrence, the track doesnt expand, nor does the positon 2 velocity change)
//just question Can the solution be expanded by higher distance displacement time-derivatives ?
If you solve this, you are wizard by my standarts. I have met people like this in my life and they are always fascinating to me. Thank you all