Scholarlink

Abstract <p>The motion of a heavy point (bead) along a curve fixed in a rigid body performing a planar instantaneous translational motion is considered. It is assumed that such a motion of the body is provided by means of two identical suspensions, both fixed ends of which are located at the same horizontal line. The movable ends are fixed in the body so that the line containing the points of these attachment points remains horizontal during the motion. In other words, we are talking about swings moving in such a way that their seat makes an instantaneous translational motion. Assuming that the bead performs a predetermined relative periodic motion along the curve, the non-existence of the first integral of the equations of motion is investigated. Within the analysis, the Poincaré mapping of the phase plane onto itself, regions of chaotic motion are identified. Some periodic movements are found and the necessary conditions for their stability are investigated.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Swings Actuated by the Relative Motion of the Bead: Regular and Chaotic Dynamics

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • A. A. Burov,
  • V. I. Nikonov

摘要

Abstract

The motion of a heavy point (bead) along a curve fixed in a rigid body performing a planar instantaneous translational motion is considered. It is assumed that such a motion of the body is provided by means of two identical suspensions, both fixed ends of which are located at the same horizontal line. The movable ends are fixed in the body so that the line containing the points of these attachment points remains horizontal during the motion. In other words, we are talking about swings moving in such a way that their seat makes an instantaneous translational motion. Assuming that the bead performs a predetermined relative periodic motion along the curve, the non-existence of the first integral of the equations of motion is investigated. Within the analysis, the Poincaré mapping of the phase plane onto itself, regions of chaotic motion are identified. Some periodic movements are found and the necessary conditions for their stability are investigated.