The design of multibody systems involves high fidelity and reliable techniques and formulations that should help the analyst to make reasonable decisions. Given that constrained equations of motion for the simplest of multibody systems are highly nonlinear, determining the sensitivity terms is a computationally intensive and complex process that requires the application of special procedures. In this article, two novel Hamiltonian‐based approaches are presented for efficient sensitivity analysis of general multibody systems. The developed direct differentiation and the adjoint methods are based on constrained Hamilton's canonical equations of motion. This formulation provides solutions, which are more stable as compared to the results of direct integration of equations of motion expressed in terms of accelerations due to a reduced differential index of the underlying system of differential‐algebraic equations and explicit constraint imposition at the velocity level.The proposed Hamiltonian based methods are both capable of calculating the sensitivity derivatives and keeping the growth of constraint violation errors at a reasonable rate. The Hamiltonian‐based procedures derived herein appear to be good alternatives to existing methods for sensitivity analysis of general multibody systems.

中文翻译：

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哈密​​顿直接微分和伴随方法进行多体系统敏感性分析

多体系统的设计涉及高保真度和可靠的技术及公式，这将有助于分析师做出合理的决定。鉴于最简单的多体系统的受约束运动方程是高度非线性的，因此确定敏感度项是一个计算量大且复杂的过程，需要应用特殊程序。在本文中，提出了两种新颖的基于Hamiltonian的方法，可以对通用多体系统进行有效的灵敏度分析。所发展的直接微分法和伴随方法是基于受约束的汉密尔顿经典运动方程。此公式提供了解决方案，与基于加速度表示的运动方程直接积分的结果相比，该方法更稳定，这是由于基础的微分代数方程组的微分指数减小以及在速度水平上施加了明确的约束所致。既可以计算灵敏度导数，又可以使约束违规误差的增长保持在合理的水平。本文推导的基于哈密顿量的方法似乎是现有的通用多体系统敏感性分析方法的替代方案。所提出的基于哈密顿方法的方法既能够计算灵敏度导数，又能够以合理的速率保持约束违规误差的增长。本文推导的基于哈密顿量的方法似乎是现有的通用多体系统敏感性分析方法的替代方案。所提出的基于哈密顿方法的方法既能够计算灵敏度导数，又能够以合理的速率保持约束违规误差的增长。本文推导的基于哈密顿量的方法似乎是现有的通用多体系统敏感性分析方法的替代方案。