Numerical integration of multibody mechanical systems using Baumgarte's constraint stabilization method

Abstract The object of this study is to solve the stability problem for the numerical integration of constrained multibody mechanical systems using Baumgarte's Constraint stabilization method. The dynamic equations of motion of the constrained multibody mechanical system are mixed differential‐algebraic equations (DAE). In applying numerical integration methods to these equations, constrained equations and their first and second derivatives must be satisfied simultaneously. That is, the generalized coordinates and their derivatives are dependent. Direct integration methods do not consider this dependency and constraint violation occurs. To solve this problem, Baumgarte proposed a constraint stabilization method in which a position and velocity terms were added in the second derivative of the constraint equation. The disadvantage of this method is that there is no reliable method for selecting the coefficients of the position and velocity terms. Improper selection of these coefficients can lead to erroneous results. In this study, stability analysis methods in digital control theory are used to solve this problem. Correct choices of coefficients for the Adams‐Bashforth and Adams‐Moulton predictor‐corrector methods with different coefficients in different stages are found.

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