When the analog stick snaps back to center it is snapping back to zero. Yes it is counted as input, input to rest position. Yes there is a software element in modern hardware to dampen “overtravel” in HOTAS and steering wheel controllers, as well as typical gaming controllers. If you google “joystick sensitivity curves” you can find more info. Input devices like computer mice have this as well. It is handled by software and can be googled under “mouse acceleration.” If you have noticed that you haven’t needed to “lift and drag” your mouse in awhile like earlier computers required, this is why. I hope this helps you in your curiosity.
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