A Sequential Integration Method

[+] Author and Article Information
Liang-Wey Chang

Department of Mechanical Engineering, Naval Postgraduate School, Monterey, CA 93943

James F. Hamilton

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Dyn. Sys., Meas., Control 110(4), 382-388 (Dec 01, 1988) (7 pages) doi:10.1115/1.3152700 History: Received June 01, 1987; Online July 21, 2009


This paper presents a method for simulating systems with two inertially coupled motions, i.e., a slow motion and a fast motion. The equations of motion are separated into two sets of coupled nonlinear ordinary differential equations. For each time step, the two sets of equations are integrated sequentially rather than simultaneously. Explicit integration methods are used for integrating the slow motion since the stability of the integration is not a problem and the explicit methods are very convenient for nonlinear equations. For the fast motion, the equations are linear and the implicit integrations can be used with guaranteed stability. The size of time step only needs to be chosen to provide accuracy of the solution for the modes that are excited. The interaction between the two types of motion must be treated such that secular terms do not appear due to the sequential integration method. A lumped model of a flexible pendulum will be presented in this paper to illustrate the application of the method. Numerical results for both simultaneous and sequential integration are presented for comparison.

Copyright © 1988 by ASME
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