A Unified Approach to Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

We propose a unified approach to dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a nonminimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in the three-dimensional space. This leads to a set of differential-algebraic equations with constant mass matrix 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 that yields realistic results for long-time simulations and accommodates nonconservative forces and 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 multifunctional structures.