001436020 000__ 04021cam\a2200565\i\4500
001436020 001__ 1436020
001436020 003__ OCoLC
001436020 005__ 20230309004005.0
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001436020 020__ $$a9789811606885$$q(electronic bk.)
001436020 020__ $$a9811606889$$q(electronic bk.)
001436020 020__ $$z9789811606878$$q(print)
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001436020 0247_ $$a10.1007/978-981-16-0688-5$$2doi
001436020 035__ $$aSP(OCoLC)1247845706
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001436020 049__ $$aISEA
001436020 050_4 $$aQA805
001436020 08204 $$a515/.39$$223
001436020 1001_ $$aIwai, Toshihiro,$$eauthor.
001436020 24510 $$aGeometry, mechanics, and control in action for the falling cat /$$cToshihiro Iwai.
001436020 264_1 $$aSingapore :$$bSpringer,$$c[2021]
001436020 300__ $$a1 online resource (x, 182 pages) :$$billustrations (some color)
001436020 336__ $$atext$$btxt$$2rdacontent
001436020 337__ $$acomputer$$bc$$2rdamedia
001436020 338__ $$aonline resource$$bcr$$2rdacarrier
001436020 4901_ $$aLecture notes in mathematics,$$x0075-8434 ;$$vvolume 2289
001436020 504__ $$aIncludes bibliographical references and index.
001436020 5050_ $$a1 Geometry of many-body systems -- 2 Mechanics of many-body systems -- 3 Mechanical control systems -- 4 The falling cat -- 5 Appendices.
001436020 506__ $$aAccess limited to authorized users.
001436020 520__ $$aThe 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.
001436020 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 27, 2021).
001436020 650_0 $$aMechanics.
001436020 650_0 $$aGeometry.
001436020 650_0 $$aMany-body problem.
001436020 650_6 $$aMécanique.
001436020 650_6 $$aGéométrie.
001436020 650_6 $$aProblème des N corps.
001436020 655_0 $$aElectronic books.
001436020 77608 $$iPrint version:$$z9811606870$$z9789811606878$$w(OCoLC)1235416042
001436020 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2289.$$x0075-8434
001436020 852__ $$bebk
001436020 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-16-0688-5$$zOnline Access$$91397441.1
001436020 909CO $$ooai:library.usi.edu:1436020$$pGLOBAL_SET
001436020 980__ $$aBIB
001436020 980__ $$aEBOOK
001436020 982__ $$aEbook
001436020 983__ $$aOnline
001436020 994__ $$a92$$bISE