At the end of each time step, violated constraints equations are corrected as explained in Geometric Correction. However, this correction perturbs the dynamics of the system and may introduce artificial energy to the system, which leads to vibrations when flexible bodies are involved. These artificial vibrations cause the time integration method to use tight time steps and more iterations which leads to long simulation times. The Stabilized Generalized-α method remedies this issue.

The equations of the dynamics are discretized as in Equation 5–59. A new Lagrange multiplier is introduced which satisfies the position-level constraints equations:

(5–65)

Where U_n represents the position gap needed to vanish the violation g(q_n). The correction of this position drift is achieved using:

(5–66)

This correction is followed by another dynamics solve using Equation 5–59. In this way, both the dynamics and the applied constraints are satisfied, which leads to more stable numerical systems.

Compared to the Generalized-α method, the Stabilized Generalized-α method uses larger average time steps and needs less iterations to converge.