The general frame or these approximations is known as "secular approximation", that can be formulated as "Fast oscillating terms do 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.
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