High Performance Multibody Simulations via Symbolic Equation Manipulation and Kane's Method

The need to simulate motions of complicated aerospace vehicles has led to widespread development of practical multi body simulation codes. Most currently available programs are, however, difficult to use and expensive to run. In this paper we describe a new approach to multibody simulations offering significant improvements in run time performance and usability. The use of Kane's formulation for the equations of motion, together with symbolic equation manipulation techniques, is shown to provide a powerful method for treating multibody prob­ lems. A multibody program, SD/EXACT, based on these ideas has been implemented and is described. Several examples are included which illustrate application of the program to various multibody systems and provide performance comparisons with earlier methods. We argue that this technique for developing multibody simulations closely parallels the approach taken by a human dynamicist when developing a high-performance simulation by hand. We then show by direct measurement that SD/EXACTcan produce simulations whose performance is comparable to the best hand-developed simulations, while conventional multibody programs can lead to simulations with execution times as much as an order of magnitude higher. Implementation considerations and chosen methods are presented for the equation formulation, symbolic equation manipulation and the program user interface. We conclude by observing that the techniques described in the paper are applicable to a much broader range of engineering problems than just multibody dynamics.

[1]  R. Roberson,et al.  A dynamical formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control. , 1966 .

[2]  W. Hooker.  A set of r dynamical attitude equations for an arbitrary n-body satellite having r rotational degrees of freedom , 1970 .

[3]  Wilfred J. Hansen.  User engineering principles for interactive systems , 1972, AFIPS '71 (Fall).

[4]  H. Frisch.  A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses , 1974 .

[5]  P. W. Likins,et al.  Attitude dynamics simulation subroutines for systems of hinge-connected rigid bodies , 1974 .

[6]  Peter W. Likins,et al.  Point-connected rigid bodies in a topological tree , 1975 .

[7]  W. Hooker.  Equations of motion for interconnected rigid and elastic bodies: A derivation independent of angular momentum , 1975 .

[8]  J.Y.L. Ho,et al.  Direct Path Method for Flexible Multibody Spacecraft Dynamics (Originally schedulled for publication in the AIAA Journal) , 1977 .

[9]  David A. Levinson,et al.  Equations of Motion for Multiple-Rigid-Body Systems via Symbolic Manipulation , 1977 .

[10]  W. Jerkovsky.  The Structure of Multibody Dynamics Equations , 1978 .

[11]  Thomas R. Kane,et al.  Formulation of Equations of Motion for Complex Spacecraft , 1980 .

[12]  Thomas R. Kane,et al.  The Use of Kane's Dynamical Equations in Robotics , 1983 .

[13]  Allen Newell,et al.  The psychology of human-computer interaction , 1983 .

[14]  R. Singh,et al.  Dynamics of flexible bodies in tree topology - A computer oriented approach , 1985 .

[15]  Richard J. Fateman.  Comments on SMP , 1985, SIGS.