标题： 弱非完整系统中非线性效应的小自由度 显示英文标题

标题： Nonlinear Effects in a Weakly Nonholonomic Systems With a Small Degrees of Freedom

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。 考虑了依赖于小参数的非完整约束的机械系统。 假设当这个参数为零时，这些系统的约束变为可积的；即，在这种情况下，我们有一个由几个任意积分常数决定的完整系统族。 我们将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，可以通过归一化方法来研究这类系统的行为。 这类系统的 behaviour 可以表示为一个略微修改的完整系统运动与缓慢变化的先前积分常数的组合（越界效应）。 在本文中，我们描述了几种自由度较小的非完整系统中的相应效应。 显示英文摘要

摘要： In 1986 Ya.V. Tatarinov presented the foundations of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that for zero value of this parameter 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 normalization methods. The behavior of such a system can be represented 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 corresponding effects in a several nonholonomic systems with a small degrees of freedom.