133 衝突振動系の定常解 : 厳密証明

概要

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In this paper, we propose the exact derivation method of all stationary solutions for an impact oscillator system, and clarified its mathematical structure. First, deriving process and functional structure of the stationary solution for linear system are reconsidered, and exact definition of stationary solution for the impact oscillator is given. 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. Some related formura, such as zero summation property of pseudo feedback responses, are also derived. The derived representations of stationary solution are natural extension of that of linear system to nonlineary system globaly. Besides, this representation perfectly prescribes all mathematical forms of the stationary solution include chaotic case. Finally, it is shown that stationary solutions are coinside with that of linear system in the eternal future and the eternal past.
一般社団法人日本機械学会の論文
2002-09-13