The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks (developed for ODEs) unusable. The appearance of these difficult-toexplain and unexpected problems leads to methods that arise heavy numerical damping for avoiding them. This has the undesired consequences of lack of convergence of the methods, along with a need of smaller stepsizes. In this paper a new approach is presented. The algorithm presented here allows us to avoid the interference of the constraints in the integration, thus allowing the linear criteria to be applied. In order to do so, the integrator is applied to a set of instantaneous minimal coordinates that are obtained through the application of the null space. The new approach can be utilized along with any integration method. Some experiments using the Newmark method have been carried out, which validate the methodology and also show that the method behaves in a predictable way if one considers linear stability criteria.

翻译：处理高阶微分代数方程（DAEs）的积分器稳定性是一个重要问题。常规算法会引发线性分析无法预测的不稳定性，导致针对常微分方程（ODEs）开发的常规检验方法失效。这些难以解释且意料之外的问题促使人们采用强数值阻尼方法加以规避，但由此带来了方法收敛性不足以及所需步长更小的不良后果。本文提出了一种新方法。该算法通过避免约束对积分的干扰，使得线性判据得以应用。为此，积分器被应用于一组通过零空间方法获得的瞬时极小坐标。该新方法可与任意积分方法配合使用。通过采用Newmark方法进行的实验验证了该方法的有效性，并表明若考虑线性稳定性判据，该方法的表现具有可预测性。