ABSTRACT
In this chapter we apply the theorems on the averaging on the infinite interval that were proved in Chapter 9 to the investigation of the stability of equilibria of pendulum systems with oscillating pivots. The approach in the application of Theorems 9.1, 9.3 and 9.4 consists of the following steps. The equations of motion of a system under investigation are written in Lagrange form. Next, we go to the Hamiltonian form of writing the equations of motion. We introduce a small parameter and make a change to a fast time. Thus, we obtain a system in standard form. The problem of the stability of equilibria is solved using the averaged equations in the first approximation.
