By comparing 3 constituents of Orion A (gas, protostars, and pre-main-sequence stars), both morhologically and kinematically, we derive the following. The gas surface density near the integral-shaped filament (ISF) is well represented by a power law, Sigma(b)=72 Msun/pc^2(b/pc)^{-5/8} for our entire range, 0.05<b/pc<8.5, of distance from the filament ridge. Essentially all protostars lie on the ISF or other filament ridges, while almost all pre-main-sequence stars do not. Combined with the fact that protostars move <1 kms relative to the filaments while stars move several times faster, this implies that protostellar accretion is terminated by a slingshot ejection from the filaments. The ISF is the 3rd in a series of star bursts that are progressively moving south, with separations of a few Myr in time and 3 pc in space. This, combined with the filaments observed undulations (spatial and velocity), suggests that repeated propagation of transverse waves thru the filament is progressively digesting the material that formerly connected Orion A and B into stars in discrete episodes. We construct an axially symmetric gas density profile rho(r)=16 Msun/pc^3(r/pc)^{-13/8}. The model implies that the observed magnetic fields are supercritical on scales of the observed undulations, suggesting that the filaments transverse waves are magnetically induced. Because the magnetic fields are subcritical on scales of the filament on larger scales, the system as a whole is relatively stable and long lived. Protostellar ejection occurs because the gas accelerates away from the protostars, not the other way around. The model also implies that the ISF is kinematically young, which is consistent with other lines of evidence. The southern filament has a broken power law, which matches the ISF profile for 2.5<b/pc<8.5, but is shallower closer in. It is also kinematically older than the ISF.
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