Consider a rocket launch from Kennedy, latitude 28.5 deg, to a target orbital inclination of 50.6 degrees for rendezvous with the ISS.
The launch azimuth for this orbital inclination is roughly 45 deg north of due east.
At T0, inertial velocity is roughly 400 m/s due east imparted by earth's rotation.
At orbital insertion, inertial velocity is roughly 7,800 m/s pointing northeast.
In between, the velocity vector must gradually transition between its initial eastward direction to its final northeastward direction.
This means the cross-product of the rocket's position and velocity vectors, r x v, which defines the eventual orbital plane, is constantly evolving all the way up to orbit.
So I want to say that at T0, r x v will indicate an inclination angle of 28.5 degrees, and that only at orbit insertion will r x v indicate an inclination of 51.6 deg...
Is this correct? Does it take the whole launch for the inclination angle to reach its target orbital value? (Pretend for a moment that the orbital inclination angle means something even before you reach orbit---does it take the whole launch for that value to stabilize?)