Four propellers produce thrust F_i in a direction perpendicular to the plane of rotation of propellers, as shown in the following diagram. This thrust is proportional to the square of the angular velocity of the propeller:

These forces are shown in action in the following diagram:

As the propellers rotate, they create the reaction Moments M_i on the quadcopter, around the z axis . This reaction moments is proportional to the square of the angular velocity of the propeller. The thrust produced by the opposite pair of propellers produces moments M_x and M_y respectively. These moments are given by a difference of forces multiplied by the length between the two propellers. Last but not the least, there is the force of gravity, which is always acting in a downward direction.

The motion of the quadcopter can be analyzed by Newton's Second Law of Motion:

For linear motion:

For angular/rotation motion: