Application of the modified Lagrange functions to account for the additional constraints in mechanical systems

Presents the results of research on the theoretical foundations of the use of modified Lagrange functions, developed in numerical optimization methods to account for the additional links in the holonomic mechanical systems. It is shown that this problem is equivalent to the development of a Применение метода модифицированных функций Лагранжа. custom PID in the theory of adaptive control. The problems of constructing stable recursive algorithms for estimating the parameters of the modified Lagrange functions for the propulsion of mechanical systems along with additional constraints. This methodology taking into account additional geometric and kinematic constraints allows you to expand the scope of numerical simulation algorithms, developed for mechanical systems with the structure of a tree, on a system with closed kinematic chains. Comparative efficiency of the method is shown by test example.