An Improved Symbolic Manipulation Technique for the Simulation of Nonlinear Dynamic Systems With Mixed Time-Varying and Constant Terms

[+] Author and Article Information
C. R. Witham

M. B. Associates, San Ramon, Calif.

S. Dubowsky

School of Engineering and Applied Science, University of California, Los Angeles, Calif.

J. Dyn. Sys., Meas., Control 99(3), 157-166 (Sep 01, 1977) (10 pages) doi:10.1115/1.3427097 History: Received May 09, 1977; Online July 13, 2010


The time domain behavior of nonlinear dynamic systems often is obtained by numerical integration on the digital computer. These solutions are usually expensive and limit the scope of the dynamic study. The proposed improved technique results in a substantial increase in the computational efficiency by using automatic symbolic manipulation to generate explicit equations of motion algebraically prior to numerical integration. A model is presented which considers the effects of the presence of time-invariant and time-varying symbolic terms and of the sparsity of system elements to provide analytical guidelines for the use of this technique. A number of case studies including typical computational costs are presented.

Copyright © 1977 by ASME
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