Studies on Modeling and Performance Analysis of Nonlinear Dynamic Systems

本研究于1988年5月至1981年3月进行。本文的目的是对非线性动态系统的建模和性能分析进行系统的研究。本文的主要研究成果如下：1.非线性动力系统的涨落分析及无穷维同伦方法的研究通过发展非确定性算子理论，阐明了涨落对非线性系统响应的若干性质。此外，还建立了数值分析包括无穷维系统在内的非线性系统的无穷维同伦方法.非线性电路的局部和全局分叉现象非线性电路分析中的全局分叉现象的一些性质已被阐明。此外，通过计算机模拟和电路实验，还观察到了一些有趣的分岔现象.非线性动力系统的数值方法发展了一种计算非线性电路、非线性规划、通道以及一类非线性方程的全部解的有效算法.动力学系统的建模及其应用利用键合图的概念，提出了一类动力学系统的自动建模方法。在此基础上，建立了柔性多体动力学分析的有效模型和数值积分方法。

This scientific research has been done during the period from May, 1988 to March 1981. The purpose of the research is to do systematic research on modeling and performance analysis of nonliear dynamic systems. The following are main results obtained by the research :1. Analysis of Fluctuation of Nonlinear Dynamic Systems and Studies on Infinite Dimensional Homotopy MethodA number of properties have been clarified on response of fluctuations to nonlinear systems by developing a theory of non-deterministic operators. Moreover, an infinite dimensional homotopy method has been established for numerically analyzing nonlinear systems including infinite dimensional systems.2. Local and Global Bifurcation Phenomena of Nonlinear CircuitsA number of properties have been clarified on the global bifurcation phenomena in nonlinear circuits analysis. Moreover, a number of interesting bifurcation phenomena have been observed by computer simulations and circuit experiments.3. Numerical Method of Nonlinear Dynamic SystemsAn efficient algorithm has been developed for caluculating solutions of nonlinear circuits, nonlinear programming, channels, and all solutions of a certain class of nonlinear equations.4. Modelig of Dynamical Systems and Its ApplicationBy using concept of the bond graph an automatic modeling method is presented for a class of dynamical systems. Based on this, an efficient modeling and a numerical integral method have been established for analyzing flexible multibody dynamics.