Operational Space Impulse Momentum Algorithm for Flexible Multibody Systems With Generalized Topologies

This paper presents a new methodology for modeling discontinuous dynamics of flexible and rigid multibody systems based on the impulse momentum formulation. The new methodology is based on the seminal idea of the divide and conquer scheme for modeling the forward dynamics of rigid multibody systems. While a similar impulse momentum approach has been demonstrated for multibody systems in tree topologies, this paper presents the generalization of the approach to systems in generalized topologies including many coupled kinematically closed loops. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The generalized impulse momenta equations of flexible bodies are derived using a projection method.