This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in three-dimensional space. This leads to a set of differential-algebraic equations with a constant mass matrix and free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme which yields realistic results for long-time simulations, and accommodates non-conservative forces as well as boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-$k$ general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multi-functional structures.

翻译：本文提出一种通用方法，用于对含刚性杆及任意形状刚体的广义张拉整体结构进行动力学建模与仿真。为消除三维空间中刚体与刚性杆的异构性，采用自然坐标作为非最小描述形式，通过基本点与基向量的不同组合进行表征。该方法导出一组常质量矩阵且不含三角函数的微分代数方程，并推导了线性化动力学公式以实现静态平衡附近的模态分析。针对非线性动力学的数值分析，我们提出一种改进的辛积分方案，既能获得长时间仿真的可靠结果，又可兼容非保守力与边界条件。数值算例验证了该方法对复杂工况下Class-1至$k$类广义张拉整体结构的动力学模拟有效性，涵盖动态外载荷、缆索展开及移动边界等场景。新型张拉整体结构亦为创造多功能结构提供了新范式。