I'm trying to find the optimal-time trajectory for an object (point mass) from point
p0 with initial velocity
v0 to point
p1 with velocity
v1. I'm considering a simple environment without any obstacles to move around. The only constraint is a maximum acceleration in any direction of
a_max and optionally a maximum speed of
This is easy to work out in 1D but I struggle with the solution 2D and 3D. I could apply the 1D solution separately to each dimension, but this would only limit acceleration and speed in a single dimension. The actual acceleration might be larger in multiple dimensions.
Are there any textbook, closed-form solutions to this problem? If not, how can I solve this in a discrete-event simulation?