I need to calculate the movement of an object that is slowing down to approach its destination while turning. Calculating the linear stopping distance and deceleration is straightforward. However if the object is not pointing at the destination, and has a limited rotation speed, makes this more complicated. For example imagine it starts pointing 90 degrees off the target: its rotation will increase the distance to the target.
The turning circle increases the distance to the target, but decelerating makes the subsequent turning circle tighter, and I'm not sure how to take in to account both factors.
Basically I have the following information:
and I need to calculate the distance (or time) to the target. What is the calculation for that?
I can also see that if the starting speed is too high, it may not be solvable - in which case it would be useful to also calculate the maximum possible speed.