Numerical analyses of multi-body systems have wide applications in spacecraft, robot, and vehicle engineering. Stability of numerical solution process has being a main concern of scholars and engineers in these fields. However, almost none of ��absolutely stable�� can guarantee the stability. In the project, we will explore the physical meaning of the numerical solution, and regard the approximation of the movement of systems during small time interval as a kind of artificial constraint imposed on the systems. Consequently, errors induced by the approximation can be studied through the corresponding constraint reactive forces. The aim of the project is to find a way to control the artificial forces in order to obtain accurate and stable numerical solutions.