Abstract
In this paper, we propose the exact derivation method of all stationary solutions for an zero stiffness impact oscillator system, and clarified its mathematical structure. First, deriving process and functional structure of stationary solution for linear system are reconsidered, and extend to stationary solution for zero stiffness impact oscillator. Second, we gave a rigorous proof that the global representation of stationary solution which had been derived formerly by authors intuitive manner is actualy stationary solution. The derived representations are natural extension of stationary solution for linear system for nonlineary system globaly. Besides, this representation perfectly prescribes all mathematical forms of the stationary solution include chaotic case.
