Stability and Accuracy Analysis of Baumgarte’s Constraint Violation Stabilization Method

[+] Author and Article Information
S. Yoon

Korea institute of Aeronautical Technology, Korean Air, 118, 2-ka, Namdaemun-ro, Chung-ku, Seoul, Korea

R. M. Howe, D. T. Greenwood

Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109

J. Mech. Des 117(3), 446-453 (Sep 01, 1995) (8 pages) doi:10.1115/1.2826699 History: Received September 01, 1991; Revised August 01, 1993; Online December 11, 2007


When Baumgarte’s Constraint Violation Stabilization Method (CVSM) is used in the simulation of Lagrange equations of motion with holonomic constraints, it is shown that, with suitable assumptions on the integration step size h and the eigenvalues (λ’s) of the linearized system, the constraint variables are effectively integrated by the same algorithm as that used for the state variables. A numerical stability analysis of the constraint violations can be performed using this so-called pseudo-integration equation. A study is also made of truncation errors and their modeling in the continuous time domain. This model can be used to determine the effectiveness of various constraint controls and integration methods in reducing the errors in the solution due to truncation errors. Examples are presented to illustrate the use of a higher-order truncation error model which leads to an accurate quantitative steady-state analysis of the constraint violations.

Copyright © 1995 by The American Society of Mechanical Engineers
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