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Titlebook: Geometry, Mechanics, and Control in Action for the Falling Cat; Toshihiro Iwai Book 2021 The Editor(s) (if applicable) and The Author(s),

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發(fā)表于 2025-3-21 17:30:54 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Geometry, Mechanics, and Control in Action for the Falling Cat
編輯Toshihiro Iwai
視頻videohttp://file.papertrans.cn/384/383848/383848.mp4
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
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Geometry, Mechanics, and Control in Action for the Falling Cat;  Toshihiro Iwai Book 2021 The Editor(s) (if applicable) and The Author(s),
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
關(guān)鍵詞Connection theory in differential geometry; Vibrations and rotations of many-body systems; Vanishing a
版次1
doihttps://doi.org/10.1007/978-981-16-0688-5
isbn_softcover978-981-16-0687-8
isbn_ebook978-981-16-0688-5Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor
The information of publication is updating

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發(fā)表于 2025-3-21 21:17:01 | 只看該作者
Book 2021gid 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
板凳
發(fā)表于 2025-3-22 01:32:40 | 只看該作者
Geometry, Mechanics, and Control in Action for the Falling Cat
地板
發(fā)表于 2025-3-22 07:31:43 | 只看該作者
Continuum Mechanics of Plasticity,This chapter deals with the geometric setting for planar and spatial many-body systems on the basis of connection theory. Rather, the contents of this chapter may be of practical help in understanding the connection theory.
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發(fā)表于 2025-3-22 12:30:08 | 只看該作者
Elastography in Liver-Transplanted PatientsIn this chapter, the equations of motion for a free rigid body are treated on the variational principle, which forms a basis for deriving the equations of motion of spatial many-body systems on the variational principle.
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發(fā)表于 2025-3-22 13:30:45 | 只看該作者
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發(fā)表于 2025-3-22 20:56:08 | 只看該作者
Hans Winter,Klaus Michaelis,Max SimonOn the basis of the geometry, mechanics, and control studied in the previous chapters, the falling cat is modeled and analyzed to make the cat model turn a somersault under a well-designed control input.
8#
發(fā)表于 2025-3-22 22:24:23 | 只看該作者
Tribologie: Reibung, Verschlei?, SchmierungThese appendices contain some remarks on basic notions from differential geometry and advanced materials for many-body systems, together with a review of Newton’s law of gravitation.
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發(fā)表于 2025-3-23 03:14:44 | 只看該作者
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發(fā)表于 2025-3-23 09:00:15 | 只看該作者
Mechanics of Many-Body Systems,In this chapter, the equations of motion for a free rigid body are treated on the variational principle, which forms a basis for deriving the equations of motion of spatial many-body systems on the variational principle.
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