Abstract: When simulating the dynamics of muti-rigid-body systems, the Index-1 differential-algebraic equations (DAEs) only consider the acceleration constraint equations, leading to the constraints violation at position and velocity levels. In this work, the dynamic equations on SE(3) are offered based on the Hamilton’s principle. Then four constraint stabilization methods on SE(3) are introduced: the Baumgarte stabilization method, the penalty method, the augmented Lagrangian formulation and constraint violation stabilization upgraded method. The motion equations with four kinds of constraint stabilization methods on SE(3) are respectively simulated by RKMK(Runge-Kutta Munthe-Kass) method. Finally, two numerical examples, including a spatial double pendulum and a crank slider mechanism, are presented. The result related to constraints violation at position and velocity levels and conservation of the total energy are analyzed. It is concluded that the four constraint stabilization methods on SE(3) are effective for preserving structure and energy conservation where RKMK is employed. Compared with the other three methods, ALF method on SE(3) can provide better numerical accuracy, smaller constraints violation at both position and velocity levels. Baumgarte stabilization method on SE(3) can balance the calculation efficiency and accuracy well.