Symbolic vector/dyadic multibody formalism for tree-topology systems

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 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.

Numerical Continuation of Solutions and Bifurcation Analysis in Multibody Systems Applied to Motorcycle Dynamics

“…In the presented approach, the equations of motion are generated in a symbolic form by the multibody dynamics program AutoSim [16][17][18][19]. This program can handle systems of rigid bodies that are interconnected by prismatic, revolute, and spherical joints or combinations of these and are arranged in a tree, which means that the graph of connections has a tree structure.…”

Vehicle Models for RTS Applications

“…AutoSim takes as input a description of the multibody system mostly in geometric terms such as body degrees of freedom (DOF), point locations, directions of force vectors, etc. [5,6]. From this information, it derives equations of motion as ODEs, and generates computer source code (C or Fortran) to solve them.…”

Symbolic computer language for multibody systems

“…18 The multibody formalism presently used in AUTOSIM is based on tree-topology systems. The basics of the formalism are described in a companion paper, 19 and extensions that allow AUTOSIM to handle nonholonomic constraints and kinematical closed loops are described in Ref. 20.…”