How to determine the miss of an aircraft?

Question

Mathematics

Hello!
There are initial data:
X, Y, Z of the aircraft at the moment of the start of the maneuver;
The direction of the velocity vector (by slope and direction) at the moment of the start of the maneuver;
The direction of the axis (by inclination and direction) at the moment of the start of the maneuver (does not coincide with the velocity vector);
Available lateral overload due to the steering controls;
The speed of the aircraft;
Longitudinal overload=0.
X,Z points on the plane of the earth, which should "get" the aircraft;
The speed vector of the point;
Point movement speed.
Maneuvering is carried out according to the method of proportional guidance.
What other input data is needed to calculate the miss of an aircraft? How can it be calculated? It is necessary to obtain the X,Z points of the fall of the aircraft.

Answer 1

If you do not need to bother with the Coriolis force, air resistance, and even more so aerodynamics, then consider the intersection of the parabola with the ground plane. You solve the problem on the plane along which the projectile moves (i.e., the problem is two-dimensional), the plane itself is located through the direction vector of the aircraft.
ps if the device flies with the engines turned on, then first solve the problem as if they were turned off, and then give a correction based on them. of course, if the engines operate with variable acceleration, then this will also have to be taken into account ...