A unified formulation for massively parallel rigid multibody dynamics of O(log₂n) computational complexity

A novel algorithm for the solution of the inverse dynamics problem is presented and augmented to the solution of the equations of motion (EOM) for rigid multibody chains using explicit constraint components of force. The unified model corresponds to an optimal, strictly parallel, time, space, and processor lower bound solution to the dynamics of accelerated rigid multibodies, i.e., computation time of O(log₂ n) using O(n) processors for an n body system. Complex topological structures are supported in the form of multiple degree-of-freedom (DOF) joints/hinges, free-floating, hyper-branched, and/or closed-chain systems, with applications ranging from multibody molecular dynamics simulations and computational molecular nanotechnology, to real-time control and simulation of spatial robotic manipulators. In addition to the theoretical significance, the algorithms presented are shown to be very efficient for practical implementation on MIMD parallel architectures for large-scale systems.