Can someone explain to me what the axis XY?

Do you mean in my Figure ?

In aeronautical convention, generally speaking, X axis is pointing forward, Z axis is pointing downward and Y axis is pointing sideway to starboard.

There are mainly three coordinates system : 1) inertial coordinate system, 2) body-fixed coordinate system and 3) wind coordinate system.

Origin of these coordinates system are the center of mass of the aircraft.

1) Inertial coordinate system :

The Z axis is parallel to the direction of gravity, and direction of X and Y axis doesn’t matter for mechanic equations.

2) Body-fixed coordinate system :

Axes of the body-fixed coordinate system (or fuselage coordinate system) rotate with the aircraft. These axis are generally chosen so that m.o.i. Ixy=Iyz are zero which is equivalent to say that the XFZF plane is a plane of symmetry of the aircraft.

3) Wind coordinate system

The X axis of the wind coordinate system is align with the freestream velocity, and points forward. The Z axis of the wind coordinate system is pointing downward and belongs to the XFZF plane (plane of symmetry of the aircraft).

In rotary wing aircraft you must also define coordinates system relative to the rotor. It is more convenient to study rotor behavior to have the Z axis pointing upward.

To do so, I decided in GyroRotor program to swap the X and Y axis. So in GyroRotor program the YS axis is pointing forward and belongs to the XFZF plane (therefore XS=YF), the ZS axis is pointing upward (the ZS axis is the NFA) and the XS axis is pointing sideway to starboard.

Finally, in GyroRotor program the aircraft velocity is supposed to be in the YSZS plane (the slidesleep angle is zero).