| 书目名称 | Geometry, Mechanics, and Control in Action for the Falling Cat | | 编辑 | Toshihiro Iwai | | 视频video | | | 概述 | Gives undergraduate and graduate students alike a vivid idea of connection theory in action for many-body systems.Shows that geometric mechanics for many-body systems works well in dealing with the fa | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat.In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the | | 出版日期 | Book 2021 | | 关键词 | Connection theory in differential geometry; Vibrations and rotations of many-body systems; Vanishing a | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-16-0688-5 | | isbn_softcover | 978-981-16-0687-8 | | isbn_ebook | 978-981-16-0688-5Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
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发表于 2025-3-21 17:30:54
