Modeling of dynamics processes and dynamics control; [Динамика процестерiн модельдеу және байланыстарды тұрақтандыруды ескере отырып, жүйенi басқару синтезi]; [Моделирование процессов динамики и синтез управления системой с учетом стабилизации связей]

Equations and methods of classical mechanics are used to describe the dynamics of technical systems containing elements of various physical nature, planning and management tasks of production and economic objects. The direct use of known dynamics equations with indefinite multipliers leads to an increase in deviations from the constraint equations in the numerical solution. Common methods of constraint stabilization, known from publications, are not always effective. In the general formulation, the problem of constraint stabilization was considered as an inverse problem of dynamics and it requires the determination of Lagrange multipliers or control actions, in which holonomic and differential constraints are partial integrals of the equations of the dynamics of a closed system. The conditions of stability of the integral manifold determined by the constraint equations and stabilization of the constraint in the numerical solution of the dynamic equations were formulated. © 2024 The Authors.