A Study of Analysis and Design of Complex Multibody Systems by the Implcit Lagrangian Method

本研究的目的是利用隐式拉格朗日系统理论，为复杂的多体系统如人造卫星、机器人、电路等提供一种系统的分析和设计方法，使我们既能处理具有非完整约束的机械系统，也能处理具有狄拉克约束的机械系统。在本研究中，我们主要研究了以下项目：(1)结构系统的子系统分解和互连；(2)模块化隐式拉格朗日系统的动力形式化；(3)结构保持数值积分格式的离散拉格朗日-达朗贝尔原理的发展。最后，通过非线性L-C电路、机器人、非完整机械系统和航天任务设计的实例验证了所提方法的有效性。

The purpose of this research is to develop a systematic method of analysis and design for complex multibody systems such as artificial satellite, robots, electric circuits and so on by the theory of implicit Lagrangian systems, which enables us to treat mechanical systems with nonholonomic constraints as well as with Dirac constraints. In this study, we have principally investigated the following items:(1) Decomposition into subsystems and interconnection for structuring systems, (2) Dynamical formalism for moduled implicit Lagrangian systems, (3) Development of discrete Lagrange-d'Alembert principle for structure preserving a numerical integration scheme. Finally, we have shown the validity of the proposed method by some illustrative examples of nonlinear L-C circuits, robots, nonholonomic mechanical systems and space mission design.