ABSTRACT
The problem of the boundedness of motion of mechanical systems simulated by ordinary differential equations has been considered by many authors. Here we will only mention some works directly related to the investigation carried out in this chapter. In the work of Yoshizawa [1] the problem of the boundedness of solutions is considered in the context with the method of Lyapunov functions. In the work of Lakshmikantham and Leela [1] it was noted that the application of a perturbed Lyapunov function in the problem of the boundedness of motion results in the reduction of requirements to auxiliary functions in the study of nonuniform properties of motion. The extension of the conditions to perturbations of a Lyapunov function proposed in the article of Burton [1] provides an opportunity to consider the problem of the boundedness of motion of nonlinear weakly connected systems under wider assumptions on dynamical properties of subsystems.
