This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using non-minimum coordinates to simplify descriptions of the structure’s kinematics. To minimize constraint drift arising from this redundant system, the direct correction method has been employed in conjunction with a novel energy-correcting scheme that treats the total mechanical energy of the system as a supplementary constraint. The formulation has been extended to allow tensegrity structures with compressible bars, allowing for further discussion on potential choices for softer bar materials. The benchmark example involving a common tensegrity structure demonstrates the superiority of the presented formulation over Simscape Multibody in terms of motion accuracy as well as energy conservation. The effectiveness of the energy correction scheme is found to be increasing with the extent of deformations in the structure.

中文翻译：

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具有可压缩杆的张拉整体系统中约束动力学的拉格朗日方法

本文提出了一种在张拉整体框架中模拟多体动力学的拉格朗日方法，该方法能够解决节能方案中违反完整约束的问题。控制方程使用非最小坐标来描述，以简化结构运动学的描述。为了最大限度地减少由该冗余系统引起的约束漂移，直接校正方法已与一种新的能量校正方案结合使用，该方案将系统的总机械能视为补充约束。该公式已扩展为允许具有可压缩杆的张拉整体结构，从而可以进一步讨论更软的杆材料的潜在选择。涉及常见张拉整体结构的基准示例证明了所提出的公式在运动精度和能量守恒方面优于 Simscape Multibody。发现能量校正方案的有效性随着结构变形的程度而增加。