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 completely integrable Hamiltonian systems. When the small parameter is not zero, the behavior of such systems can be considered with the help of asymptotic methods representing their motion as a combination of the motion of a slightly modified holonomic system with slowly varying previous integration constants (the transgression effect). In this paper, we describe the transgression effect in the problem of motion of an almost holonomic pendulum.

中文翻译：

---

近完整摆运动问题中的海侵效应

摘要

1986 年，Ya.V. 塔塔里诺夫提出了弱非完整系统理论的基础。考虑具有取决于小参数的非完整约束的机械系统。假设当该参数的值为零时，该系统的约束变得可积；即，在这种情况下，我们有一系列完整系统，取决于几个任意积分常数。我们假设这些完整系统是完全可积的哈密顿系统。当小参数不为零时，可以借助渐近方法来考虑此类系统的行为，将其运动表示为稍微修改的完整系统的运动与缓慢变化的先前积分常数（海侵效应）的组合。在本文中，我们描述了近完整摆运动问题中的越界效应。