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