You know that a 3D analysis can often be reduced to a 2D one by suitable choice of viewpoint.
In similar fashion we can often reduce a dynamic situation to a quasi-static one by suitable choice of coordinate system (viewpoint).
Some examples:
An analysis of a rotating disk made from the point of view of an observer sitting on the disk, and therefore going round with it, is quasi- static in that we can ignore the rotational motion of the disk adding a central 'force' if necessary.
The support reaction for a drive shaft is going to be the same whatever speed the shaft is doing, or even if the shaft is actually turning at all.
In fluid flow if a 'steady state' is achieved we can ignore the dynamics of the flow for the purposes of calculating energy transfer.
Engineers are tricky individuals - they are always seeking to reduce the complexity of the maths by any trick they can invent.
go well