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Graph Theoretic Foundations of Multibody Dynamics Part II: Analysis and Algorithms.

Abhinandan Jain¹

¹Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109.

Multibody System Dynamics

|November 22, 2011

Summary

This study leverages graph theory to advance multibody dynamics. It introduces spatial kernel operator (SKO) models, demonstrating their ability to simplify complex system analyses and computations.

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Area of Science:

Multibody Dynamics
Graph Theory
Mathematical Modeling

Background:

Previous work established block-weighted adjacency (BWA) matrices for serial and tree topology multibody systems.
Notions of spatial kernel operators (SKO) and spatial propagation operators (SPO) were introduced.

Purpose of the Study:

To formalize the use of SKO models for general tree-topology multibody systems.
To demonstrate that analytical results and computational algorithms stem directly from structural properties.
To require minimal assumptions about the multibody system's nature.

Main Methods:

Formalization of spatial kernel operator (SKO) models for general tree-topology multibody systems.
Utilizing graph theory concepts to analyze the structure of spatial operators.

Main Results:

Key analytical results, including mass matrix factorization, inversion, and decomposition, hold for all SKO models.
Low-order scatter/gather recursive computational algorithms are derived from abstract-level analytical results.
A general methodology for developing SKO models is presented.

Conclusions:

SKO models provide a unified framework for analyzing diverse multibody systems.
The abstract nature of SKO models enables broad applicability.
Analytical and computational advancements are direct consequences of structural properties.