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Geometry, Mechanics, and Control in ...
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Geometry, Mechanics, and Control in Action for the Falling Cat
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Geometry, Mechanics, and Control in Action for the Falling Cat/ by Toshihiro Iwai.
作者:
Iwai, Toshihiro.
面頁冊數:
X, 182 p. 24 illus., 5 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Applications of Nonlinear Dynamics and Chaos Theory. -
電子資源:
https://doi.org/10.1007/978-981-16-0688-5
ISBN:
9789811606885
Geometry, Mechanics, and Control in Action for the Falling Cat
Iwai, Toshihiro.
Geometry, Mechanics, and Control in Action for the Falling Cat
[electronic resource] /by Toshihiro Iwai. - 1st ed. 2021. - X, 182 p. 24 illus., 5 illus. in color.online resource. - Lecture Notes in Mathematics,22891617-9692 ;. - Lecture Notes in Mathematics,2144.
1 Geometry of many-body systems -- 2 Mechanics of many-body systems -- 3 Mechanical control systems -- 4 The falling cat -- 5 Appendices.
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 cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.
ISBN: 9789811606885
Standard No.: 10.1007/978-981-16-0688-5doiSubjects--Topical Terms:
1113607
Applications of Nonlinear Dynamics and Chaos Theory.
LC Class. No.: QA641-670
Dewey Class. No.: 516.36
Geometry, Mechanics, and Control in Action for the Falling Cat
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