The transgression effect in the problem of motion of an almost holonomic pendulum

Abstract

In 1986, Ya. V. Tatarinov presented the basis of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that when the value of this parameter is zero, the constraints of such a system become integrable, i. e. in this case we have a family of holonomic systems depending on several arbitrary integration constants. We will assume that these holonomic systems are integrable hamiltonian systems. When the small parameter is not zero, the methods of perturbation theory can be used to represent, to a first approximation, the motion of the system with nonzero parameter values, as a combination of the motion of a slightly modified holonomic system with slowly varying previous integration constants (transgression effect). In this paper, we describe the transgression effect in the problem of motion of an almost holonomic pendulum.