Here's what I know: If a body moves in a circular trajectory, then the resultant of all the forces must point to the center of the circle it describes in its movement. If a body moves in a vertical loop, there will be two forces acting on it: The normal forces exerted by the track and the force of gravity. I have solved the "loop the loop problem".
But, what guarantees that, at any point, the resultant of the normal force and the gravity force will always point to the center of the circle? It is clear that the normal force will be greater than zero, so the body doesn't loose contact with the tracks (if it loops the loop). But is this enough to keep it in a circular motion?
So, what assures us that if we compose the vectors graphically, the resultant will always point to the center?