HHT METHOD WITH CONSTRAINTS VIOLATION CORRECTION IN THE INDEX 2 EQUATIONS OF MOTION FOR MULTIBODY SYSTEMS

Equations of motion for multibody system with holonomic constraints in Cartesian absolute coordinates modeling method are index 3 differential-algebraic equations (DAEs).It is high index problem for numerical integration of index 3 DAEs.The index can be reduced to 2 by taking the derivative of position constraint equations, and velocity constraint equations can be obtained.During the integration of index 3 equations of motion, the velocity constraint equations are violated, and there are some problems in the integration of high index DAEs.Firstly, HHT (Hilber-Hughes-Taylor) direct integration method is used to the numerical integration of index 2 equations of motion.The velocity constraint equations involved in the integration, and they are satisfied in the view of computer precision.However, the position constraint equations are violated.Secondly, in order to eliminate the violation, the correction method based on MoorePenrose generalized inverse theory is adopted.HHT method with constraints violation correction for index 2 equations of motion is the combination of HHT and correction method.There are no position and velocity constraints violation during the integration in the view of computer precision.No new unknown variables are introduced, and the quantity of equations in nonlinear equations from discretization is the same as index 2 equations of motion.The new integration method is validated by numerical experiments.In addition, some characteristics of HHT method, such as controlled numerical damping and second-order accuracy, are persisted by the new integration method.Finally, the quantity of nonlinear equations from discretization and computational efficiency are compared with some other methods.The advantages of the new method are illustrated.