Regular and Chaotic Rigid Body Dynamics
Regular and Chaotic Rigid Body Dynamics
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规则和混沌刚体动力学
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Otto Hahn
中科院分区：
文献类型：
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作者：
P. Richter;Otto Hahn
刚体动力学作为非平凡可积性的重点，在力学课程中讲授。然而，该领域的绝大多数问题都是不可积的。由英雄欧拉、拉格朗日、雅可比、维尔斯特拉斯、科瓦列夫斯卡娅、庞加莱和其他人开发的美丽的积分方法分散了这样一个事实，即混沌而不是规则性是规则，应该开发数值和图形方法来展示系统的真正复杂性。本文介绍了在这个方向上的尝试，重点是识别不变集的配置和动量空间，并在方便的庞加莱曲面的定义。
Rigid body dynamics is taught in mechanics courses as the highlight of non-trivial integrability. Yet the overwhelming majority of problems in the field is non-integrable. The beautiful methods of integration developed by the heroes Euler, Lagrange, Jacobi, Weierstras, Kovalevskaya, Poincare and others, distract from the fact that chaos rather than regularity is the rule, and that numerical as well as graphical methods ought to be developed to exhibit the system’s true complexity. The paper describes attempts in that direction, focusing on the identification of invariant sets in configuration and momentum space, and on the definition of convenient Poincare surfaces of section.