On equations of the kinematics and dynamics of constrained mechanical systems

Summary (translated from the Russian): "We present a method for constructing equations of kinematics and dynamics of mechanical systems that are designed for numerical realization. We construct the corresponding difference equations that guarantee computations with prescribed accuracy. We determine the equations of program constraints and of constraint perturbations. Stability of the program manifold in the numerical solutions of the equations of dynamics is achieved by the corresponding construction of equations of perturbations of program constraints. We compare the equations of the dynamics of systems with program constraints with those in the form of Lagrange equations in generalized coordinates. We consider some inverse problems of the dynamics of a rigid body."