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Dynamic Simulation Algorithm for Multibody Systems Subject to Severe Configuration Change.

The objective of this paper is to establish a computer algorithm capable of simulating dynamics of variable configuration systems based on the unified matrix approach for multibody systems of N bodies connected by M generic hinges with M g N. The system may have an arbitrary system topology, including chain, tree and closed-loop configuration. Hinge can be either a physical joint mechanism such as gimbal, ball-joint, or spring-damper, or a hypothetical connecting point of two adjacent bodies as in case of docking. Any change in configuration and constraint conditions has been modeled by a function dependent on time and states. The approach developed here is essentially based on the formulation of a matrix form of the linear algebraic equation to be solved simultaneously for the time derivatives of non-holonomic angular and linear momenta, and the internal non-working constraint torques and forces. The non-holonomic momenta are derived for each body referring to the angular and linear velocities with respect to the inertially fixed frame expressed in the body frame of each body. With this selection of the variables, the linear equation takes a form Ax=B, where the coefficient matrix A represents the system configuration and the constraint conditions. This approach has been proven useful in simulation, such as separation, connection, topology change, and change in constraint degrees-of-freedom.