半正定最小正特征Jacobi振动系统稳定性分析

Analysis of Jacobi Matrix Mathematical System Stability Based on Semi Positive Defiuite Minimum Positive Characteristic

在机械振动系统设计等应用领域,需要应用到基于Jacobi矩阵的数学模型进行系统稳定性分析。基于Jacobi矩阵的数学模型的振动系统稳定性分析是保证模型平稳分布和存在性的重要因素。传统的非线性微分方程半正定分析方法分析采用Jacobi矩阵进行振动系统数学建模,但当多个解之间没有相关参数时,效果较差。采用半正定最小正特征带状稀疏条件下基于Jacobi矩阵的振动系统数学模型稳定性分析,首先构建了稳定性分析的数学模型,采用过连续边界分析方法实现对稳定性的稳定误差逼近分析,根据半正定最小正特征带状稀疏条件下的微分方程代数方程组,得到Jacobi数学振动系统模型稳定解分布,为实现Jacobi振动系统数学稳定性控制提供理论依据。

In the mechanical vibration design applications, it needs the Jacobi mathematical model for stability analysis of system. Stability analysis of Jacobi mathematical model is to ensure the smooth distribution model and an important factor. Positive semi definite analysis method of nonlinear differential equations of traditional Jacobi is used in analysis model, by the method of analysis solutions of nonlinear differential equations, but when a plurality of no relevant parameters between, the effect is bad. The stability of Jacobi mathematical model of semi definite minimum positive characteristic zonal sparse conditions is analyzed, we established the mathematical model of stability analysis, the continuous boundary analysis meth-od for the stability analysis of stability of the approximation error, according to the set of differential equations and algebra-ic equations positive semi definite minimum positive characteristic zonal sparse conditions, the Jacobi mathematical model of vibration stability solution distribution is obtained. It provides a theoretical basis for stability control of the Jacobi vibra-tion mathematical model.