One method of converting these DAEs to ODEs is to replace the position constraints with the acceleration constraints, which are then numerically integrated simultaneously with the ODEs from the dynamic equations. However, during the integration process, the accumulation of numerical errors leads to violations in the position constraint equations. (Visually, the cotree joints will float apart.) Baumgarte proposed a method to stabilize these constraints, by combining the position, velocity, and acceleration constraints into a single expression:
which can be written as a linear equation in terms of the accelerations:
By integrating this expression for the accelerations, the Baumgarte parameters, α and β, act to stabilize the constraints at the position level. These parameters are set using the command:
where `Model` is the module returned from the BuildEQs command, and α and β must be given numerical values prior to numerical solution. Typical values range from 1 to 10, and depend upon the characteristics of the particular system under study.
As explained below, Baumgarte stabilization is automatically used in the exports for constrained dynamic systems. If the Baumgarte parameters are not set, default values of 0 are assumed (that is, no constraint stabilization).