We know for an object:
- Initial point O(x,y)
- Initial speed (s_x,s_y)
- Constant vector module aceleration (A)
- A point P(i,j) where we have to pass through in the future.
A point W(x, y) so the angle alpha (or only the angle alpha), formed between O and W, can be used to calculate acceleration in both axis:
Ax = A * cos(alpha)
Ay = A * sin(alpha)
so that the object passes through W.
How do I define an elliptic motion system knowing two points of the orbit (and Vo)?
I'll appreciate alternatives to design a guided rocket too.
My attempt for solving this:
Calculate module of initial point O, initial speed So, destination point D. (Aceleration module A is given)
Use these terms to calculate the time we need to arrive to D with the equation:
D = O + So*t + 1/2 A * t^2
Find out the value of alpha from this equation, knowing time:
Dx = Ox + Sox * t + 1/2 A * cos(alpha) * t^2
I tried to implement this, but for some reason it doesn't work. Should this theorically work?