Home >

news Help

Publication Information


Title
Japanese:ハイブリッド自励振動子の同期ダイナミクスの位相縮約法による解析及びその応用 
English: 
Author
Japanese: 白坂 将, 紅林 亘, 中尾 裕也.  
English: 白坂 将, 紅林 亘, Hiroya Nakao.  
Language Japanese 
Journal/Book name
Japanese:機械力学・計測制御講演論文集 
English: 
Volume, Number, Page Vol. 2013       
Published date July 2013 
Publisher
Japanese:一般社団法人日本機械学会 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Abstract Hybrid dynamical systems are utilized to describle the behavior of systems that possess some kind of mixed continuous and discrete nature. Mechanical systems that exhibit self-excited vibration with impacting behavior or stick-slip motion belong to the hybrid dynamical systems family. Phase-reduction method provides a useful framework to study synchronization properties of self-excited oscillators. The nonlinear dynamics of limit cycles can be captured quantitatively by a scalar phase equation even in high dimensions as long as the perturbation is sufficiently weak. However, the adjoint method, which provides accurate linear sensitivity of oscillator's phase to perturbations, cannot be applied to hybrid self-excited oscillators straightforwardly due to the non-smoothness of the vector field of hybrid dynamical systems. In this paper, the conventional adjoint method is extended to hybrid dynamical systems, and the validity of the proposed method is demonstrated by examples. The frequency locking behavior of the hybrid self-excited oscillators is also studied. It is confirmed that the synchronization properties of the hybrid oscillators can be well explained by the theory.

©2007 Tokyo Institute of Technology All rights reserved.