On the Equations of Kinematics and Dynamics of Constrained Mechanical Systems

The method of constructing of kinematical and dynamicalequations of mechanical systems, applied to numerical realization, isproposed in this paper. The corresponding difference equations, whichare obtained, give a guarantee of computations with given precision. Theequations of programmed constraints and those of constraintperturbations are defined. The stability of the programmed manifold fornumerical solutions of the kinematical and dynamical equations isobtained by means of corresponding construction of the constraintperturbation equations. The dynamical equations of system withprogrammed constraints are set up in the form of Lagrange equations ingeneralized coordinates. Certain inverse problems of rigid body dynamicsare considered.