20312 区分線形システムの統一理論を目指して : 切り換えのダイナミクスから重ね合わせのダイナミクスヘ(OS6 非線形現象とその応用)

概要

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We have proposed an analytical method to derive global form of general solution for vibroimpact system that is one of the fundamental piecewise linear system. This method based on pseudo-feedback approach which was introduce by authors enable us to superpose linear system solution and impulsive responses caused by equivalent impact nonlinearity in order to construct general solution for target system. According to this method, periodic, almost periodic, and chaotic solution included in stationary solution can be derived globally as bounded solution with stationary succesive impacts from infinite past to everlasting future. However, evaluation of misterious effects of initial value for infinite past to infinite future are emerged in this approach. In order to overcome this difficulty, I propose a new analytical method to evaluate initial value of infinite past by using classical series summation method dealing with divegent series. It is clarified that "Renomalization of infinity" play an essential role to extract finite physically resonable value appearing in the deriving process of periodic solution.
一般社団法人日本機械学会の論文
2005-03-17