The Brass Lip Mechanism

The brass lip mechanism functions as a pressure-controlled valve that admits a puff of air whenever the pressure is high in the mouthpiece.
Because the resonance frequency of the brass lip mechanism must nearly match the desired sounding frequency of the instrument (hopefully with support from an air column resonance at or near that frequency), the mass component of the lips cannot be ignored.

Figure 19: The brass player's lips as a mechanical oscillator blown open.
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Pressure pulses reflected back from the far end of the horn tend to force the player's lips open ... positive feedback.
While one might expect the lips to be blown closed when the mouthpiece pressure is high, it should be remembered that the mass in a mass-spring-damper system lags behind the driving force by cycle at its resonance frequency (as shown in Fig. 20). During this “lag time”, the lip valve is open and flow through the valve can augment the positive mouthpiece pressure.

Figure 20: Displacement and phase of a mass-spring-damper system.
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The player controls the resonance frequency of his/her lips via tension and mass (position) variations.
Oscillations are favored when the air column has one or more resonances that correspond to the harmonics of the fundamental pitch.
Most of the equations discussed earlier for the woodwind reed valve can also be applied to the brass lip mechanism. The primary distinction concerns the equations of lip displacement. The lips are initially closed but then blown open.
Attempts to model the lip mechanism have included both “swinging-door” and “up-down” displacement trajectories.