In this paper, a new analytical approach suitable for the stability analysis of multibody mechanical systems is introduced in the framework of Lagrangian mechanics. The approach developed in this work is based on the direct linearization of the index-three form of the differential-algebraic dynamic equations that describe the motion of mechanical systems subjected to nonlinear constraints. One of the distinguishing features of the proposed method is that it can handle general sets of nonlinear holonomic and/or nonholonomic constraints without altering the original mathematical structure of the equations of motion. While the typical state-space dynamic description associated with multibody systems leads to the definition of a standard eigenproblem, which is impractical, if not impossible, to implement in the case of complex systems, the method developed in this paper involves a generalized state-space representation of the dynamic equations and allows for the formulation of a generalized eigenvalue problem that extends the scope of applicability of the stability analysis to complex mechanical systems. As demonstrated in this investigation employing simple numerical examples, the proposed methodology can be readily implemented in general-purpose multibody computer programs and compares favorably with several other reference computational approaches already available in the multibody literature.

中文翻译：

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具有完整和非完整约束的刚性多体机械系统的稳定性分析

本文在拉格朗日力学的框架内，提出了一种适用于多体力学系统稳定性分析的新分析方法。在这项工作中开发的方法是基于微分-代数动力学方程的索引三形式的直接线性化，该方程描述了受非线性约束的机械系统的运动。所提出的方法的显着特征之一是，它可以处理非线性完整和/或非完整约束的一般集合，而无需更改运动方程的原始数学结构。尽管与多体系统相关的典型状态空间动态描述导致了标准本征问题的定义，但对于复杂系统而言，这是不切实际的，即使不是不可能的，本文开发的方法涉及动力学方程的广义状态空间表示，并允许制定广义特征值问题，从而将稳定性分析的适用范围扩展到复杂的机械系统。如本研究中使用简单的数值示例所示，所提出的方法可以轻松地在通用多体计算机程序中实施，并且可以与多体文献中已有的其他几种参考计算方法进行比较。