  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.
