The multi-body dynamics appear in a new form, as a matrix differential equation, rather than the traditional vector differential equation. The model has a constant mass matrix, and the equations are non-minimal. A specific focus of this paper is tensegrity systems. A tensegrity system requires prestress for stabilization of the configuration of rigid bodies and tensile members. This paper provides an efficient model for both static and dynamic behavior of such systems, specialized for the case when the rigid bodies are axi-symmetric rods. © 2009 SPIE.