title: Multibody graph transformations and analysis: Part I: Tree topology systems.
abstract: This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion ofspatial kernel operator(SKO)modelsfor such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on thepath-inducedproperty of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies anaggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems.
authors.affiliation: Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA.
authors.forename: Abhinandan
authors.initials: A
authors.lastname: Jain
keywords: Algorithms; Graph theory; Multibody systems