On Constructing Dynamic Equations Methods with Allowance for Atabilization of Constraints

Abstract

Based on the well-known methods of classical mechanics, the construction of dynamic equations for system using well-known constraint equations is associated with the accumulation of errors in the numerical solution and requires a certain modification to stabilize the constraints. The problem of constraint stabilization can be solved by changing the dynamic parameters of the system. It allows us to determine the Lagrange multipliers in the equations of motion and take into account possible deviations from the constraint equations. In systems with linear nonholonomic constraints, it is possible to express velocity projections in terms of the coordinate functions of the system. In this case, we can compose a system of second-order differential equations and present them in the form of Lagrange equations. Using the generalized Helmholtz conditions, one can compose the Lagrange equations with a dissipative function and ensure that the conditions for the stabilization of constraints are satisfied.