The constraint-stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics

Abstract

The implicit methods on Lie group are developed for multibody system dynamics. To avoid the violation of the displacement, velocity and acceleration constraints of the nonlinear differential-algebraic equations, the constraint-stabilized equations on Lie group are formulated. The implicit method for the Euler–Lagrange equations and the symplectic Euler method for the constrained Hamilton equations are presented. These methods can keep the stability of the displacement, velocity and acceleration constraints at the same time during the longer simulation. A three-dimensional single pendulum and a three-dimensional double pendulum are used to verify the accuracy of the constraint-stabilized Euler methods on Lie group and the orthogonality preservation of the rotation matrix.