The general frame or these approximations is known as "secular approximation", that can be formulated as "Fast oscillating terms dot not contribute to the long term evolution of the system". Implicitly this assumes that there are non vanishing slow terms that alone drive the long term evolution, where "long" means at a timescale much larger than the period of oscillations. This approximation is deeply related with adiabatic aporoximation.
Jhor
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