Multibody graph transformations and analysis |
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Authors: | Abhinandan Jain |
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Institution: | 1.Jet Propulsion Laboratory,California Institute of Technology,Pasadena,USA |
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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 of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of
the component subsystems based on the path-induced property 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 an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems. |
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