Problems of Physically Plausible Simulation of the Motion of Mechanical Systems

In this paper, the problems of plausible modeling of the motion of mechanical systems are considered. Physical systems with holonomic and nonholonomic constraints will also be considered. In this paper, variational integrators are considered. This type of integrator is an example of integrators that preserve the geometric structures of a continuous system, and as such they fall into the general class of geometric integration methods. Many long-time integration problems in science and engineering, such as solar system dynamics and molecular dynamics, involve systems that are highly non-linear and sensitive to small perturbations. In the course of the work, a variational approach to the problems of mechanics was considered, the kinematics and dynamics of mechanical systems were described using Lie groups and algebra. The Lie group variational integrator provides a robust and accessible framework for modeling mechanical systems, motion control, trajectory building, and more.