Построение уравнений динамических систем со связями

Constructing dynamical equations of constrained systems

Constructing dynamical equations of constrained systems can lead to the determining of the Lagrange multipliers. Derivatives of the constraints have to be used to determine their values. But, it is assumed that the constraint equations are first integrals of the dynamical equations. This fact can lead to the multiple deviations from the constraint equations caused by some errors of a numerical method of integration and setting initial conditions. To provide a constraint stabilization the methods of constructing differential equations with given set of partial integrals are applied. Constructing equations of perturbed constraints with an asymptotically stable trivial solution can provide a constraint stabilization during the numerical solution of dynamical equations.