東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Geometry, mechanics, and control in ...

Iwai, Toshihiro.

FindBook

Google Book

Amazon

博客來

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometry, mechanics, and control in action for the falling cat/ by Toshihiro Iwai.
作者:	Iwai, Toshihiro.
出版者:	Singapore :Springer Singapore : : 2021.,
面頁冊數:	x, 182 p. :ill. (some col.), digital ;24 cm.
內容註:	1 Geometry of many-body systems -- 2 Mechanics of many-body systems -- 3 Mechanical control systems -- 4 The falling cat -- 5 Appendices.
Contained By:	Springer Nature eBook
標題:	Mechanics. -
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. - Singapore :Springer Singapore :2021. - x, 182 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v.22890075-8434 ;. - Lecture notes in mathematics ;v.2289..

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:

525881
Mechanics.

LC Class. No.: QA805 / .I935 2021

Dewey Class. No.: 515.39

Geometry, mechanics, and control in action for the falling cat
LDR:03061nmm a2200337 a 4500 001 2240103
003 DE-He213
005 20210730110948.0
006 m d
007 cr nn 008maaau
008 211111s2021 si s 0 eng d
020 $a 9789811606885 $q (electronic bk.)
020 $a 9789811606878 $q (paper)
024 7 $a 10.1007/978-981-16-0688-5 $2 doi
035 $a 978-981-16-0688-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA805 $b .I935 2021
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 515.39 $2 23
090 $a QA805 $b .I96 2021
100 1 $a Iwai, Toshihiro. $3 3494774
245 1 0 $a Geometry, mechanics, and control in action for the falling cat $h [electronic resource] / $c by Toshihiro Iwai.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2021.
300 $a x, 182 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v v.2289
505 0 $a 1 Geometry of many-body systems -- 2 Mechanics of many-body systems -- 3 Mechanical control systems -- 4 The falling cat -- 5 Appendices.
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.
650 0 $a Mechanics. $3 525881
650 0 $a Geometry. $3 517251
650 0 $a Many-body problem. $3 525019
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Control and Systems Theory. $3 3381515
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 3134772
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v.2289. $3 3494775
856 4 0 $u https://doi.org/10.1007/978-981-16-0688-5
950 $a Mathematics and Statistics (SpringerNature-11649)