Recursive flexible multibody system dynamics using spatial operators

This paper uses spatial operators to develop new spatially recursive dynamics algorithms for #exible multibody systems. The operator description of the dynamics is identical to that for rigid multibody systems. Assumed#mode models are used for the deformation of each individual body. The algorithms are based on two spatial operator factorizations of the system mass matrix. The #rst #Newton#Euler# factorization of the mass matrix leads to recursive algorithms for the inverse dynamics, massmatrix evaluation,and composite-body forward dynamics for the system. The second #Innovations# factorization of the mass matrix, leads to an operator expression for the mass matrix inverse and to a recursive articulated#body forward dynamics algorithm. The primary focus is on serial chains, but extensions togeneral topologies are also described. A comparison of computational costs shows that the articulated#body forward dynamics algorithm is much more e#cient than the composite#body algorithm for most #exible multibody systems.