A Symbolic VectorDyadic Multibody Formalism For TreeTopology Systems-英文学习资料.pdfVIP

A Symbolic Vector/Dyadic Multibody Formalism For Tree- Topology Systems Michael W. Sayers* The University of Michigan Transportation Research Institute Abstract A multibody formalism is presented that 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 judgements 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 versus 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 spacecraft multibody system. Results shown in this paper for the example spacecraft illustrate the high computational efficiency of the simulation code. Introduction There is a large body of literature covering systematic analsis methods for mechanical systems composed of rigid bodies, which are called “multibody formalisms.” The formalisms, all based on first principles, nonetheless represent a variety of analytical approaches. Large sets of simple dynamical and algebraic constraints equations can be formed into large matrices that are handled 1 2