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| 003 | | | IISER-K |
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| 039 | | 9 | \a 202212131315 \b Siladitya \c 202212131314 \d Siladitya \c 202212131311 \d Siladitya \y 202211171152 \z Pitambar |
| 040 | | | \b eng \e rda |
| 049 | | | \a MUBB |
| 050 | | 4 | \a QA641-670 |
| 066 | | | \c $1 |
| 082 | 0 | 4 | \a 510 \b LNK4.V.2289 |
| 100 | 1 | | \a Iwai, Toshihiro, \e author. |
| 245 | 1 | 0 | \a Geometry, mechanics, and control in action for the falling cat / \c Toshihiro Iwai. |
| 264 | | 1 | \a Singapore, Singapore : \b Springer, \c [2021] |
| 264 | | 4 | \c ©2021 |
| 300 | | | \a x, 182 pages : \b illustrations (some colour) ; \c 24 cm |
| 336 | | | \a text \b txt \2 rdacontent |
| 337 | | | \a unmediated \b n \2 rdamedia |
| 338 | | | \a volume \b nc \2 rdacarrier |
| 490 | 1 | | \a Lecture notes in mathematics, \x 0075-8434 ; \v volume 2289 |
| 504 | | | \a Includes bibliographical references (pages 177-180) and index. |
| 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 Fluid dynamics. |
| 650 | | 0 | \a Geometric function theory. |
| 830 | | 0 | \a Lecture notes in mathematics (Springer-Verlag) ; \v 2289. \x 0075-8434 |
| 852 | 0 | | \b BC-BC \c STACK \h QA3 \i .L28 no.2289 \4 UMBC Library \5 Stacks |
| 852 | 0 | | \b BC-BC \c STACK \h QA3 \i .L28 no.2289 \p 31429040224523 \4 UMBC Library \5 Stacks |
| 950 | | | \a Ongoing \c 20210629 \h 1355 |
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