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Geometry, mechanics, and control in ...

Iwai, Toshihiro.

Geometry, mechanics, and control in action for the falling cat

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry, mechanics, and control in action for the falling catby Toshihiro Iwai.
Author:	Iwai, Toshihiro.
Published:	Singapore :Springer Singapore :2021.
Description:	x, 182 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mechanics.
Online resource:	https://doi.org/10.1007/978-981-16-0688-5
ISBN:	9789811606885$q(electronic bk.)

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. - Singapore :Springer Singapore :2021. - x, 182 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v.22890075-8434 ;. - Lecture notes in mathematics ;2035..

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$q(electronic bk.)

Standard No.: 10.1007/978-981-16-0688-5doiSubjects--Topical Terms:

200022
Mechanics.

LC Class. No.: QA805 / .I935 2021

Dewey Class. No.: 515.39

Geometry, mechanics, and control in action for the falling cat
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520 $a 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.
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