koobas.hobune.stream
How to move an object with a starting and ending speed and time
I need to move an object from point a to point b in an exact amount of time, and also with constraint that the object must have a defined speed at point a and point b. To simplify matters, I am only considering motion on one axis.
I have tried to write an equation of motion for the path of the object by using a polynomial to represent the acceleration of the object:
x''(t) = b + ct
and then calculating the necessary values for b and c to satisfy the constraints:
x(t_0) = p_i (the initial position)
x(t_f) = p_f (the final position)
x'(t_0) = v_i (the initial speed)
x'(t_f) = v_f (the final speed)
However, the values I found made the object first travel backward for a period of time, and then forward. I would like to find a way to move the object that meets the 4 constraints listed above with the additional constraint that the object never moves backwards (that is, a monotonic equation of motion)
Does anyone have any ideas?
