Projection Method With Minimal Correction Procedure for Numerical Simulation of Constrained Dynamics

This paper describes a numerical technique for simulating the dynamics of constrained systems, which are described generally by differential-algebraic equations. The Projection Method for index reduction of a differential-algebraic equation and a minimal correction procedure are described. This procedure ensures algebraic constraints are satisfied during the numerical integration of the reduced index system of differential equations. Two examples illustrate how the method can be utilized to solve constrained multibody and rotational dynamics problems. The efficiency and accuracy of the proposed index-reduction and minimal correction method are then evaluated.