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Symbolic vector/dyadic multibody formalism for tree-topology systems. (English) Zbl 0741.93056

Summary: A multibody formalism is presented than can be applied to automatically generate efficient equations of motion for a system of rigid bodies in a tree topology. The formalism is built on Kane’s analysis method and is described using vector/dyadic notation. In addition to defining a way to formulate equations of motion, it specifies many details of the analysis that have formerly involved judgments made by a dynamicist. These details include “rule of thumb” issues such as 1) making modeling simplifications, 2) choosing state variables, 3) introducing intermediate variables, 4) choosing coordinate systems to represent vectors, and 5) choosing recursive vs nonrecursive formulations. The formalism has been automated using a computer algebra language that supports vector/dyadic algebra, small variable simplification options, and the automated introduction of new symbols. A companion paper describes this language and provides details of an example of a spacecraft multibody system. Results shown in this paper for the example spacecraft illustrate the high computational efficiency of the simulation code.

MSC:

93C85 Automated systems (robots, etc.) in control theory

Software:

AUTOSIM
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