Geometry Mechanics And Control In Action For The Falling Cat PDF Download
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Author | : Toshihiro Iwai |
Publisher | : Springer Nature |
Total Pages | : 193 |
Release | : 2021-04-23 |
Genre | : Mathematics |
ISBN | : 9811606889 |
Download Geometry, Mechanics, and Control in Action for the Falling Cat Book in PDF, ePub and Kindle
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.
Author | : Michael J. Enos |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9780821892008 |
Download Dynamics and Control of Mechanical Systems: The Falling Cat and Related Problems Book in PDF, ePub and Kindle
This book contains a collection of papers presented at the Fields Institute workshop, ``The Falling Cat and Related Problems,'' held in March 1992. The theme of the workshop was the application of methods from geometric mechanics and mathematical control theory to problems in the dynamics and control of freely rotating systems of coupled rigid bodies and related nonholonomic mechanical systems. This book will prove useful in providing insight into this new and exciting area of research.
Author | : Yakov Eliashberg |
Publisher | : American Mathematical Soc. |
Total Pages | : 452 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780821886892 |
Download Symplectic Geometry and Topology Book in PDF, ePub and Kindle
Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author | : Luis Hernández-Lamoneda |
Publisher | : Springer |
Total Pages | : 133 |
Release | : 2018-02-26 |
Genre | : Mathematics |
ISBN | : 3319714287 |
Download Geometrical Themes Inspired by the N-body Problem Book in PDF, ePub and Kindle
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.
Author | : Robert A. Meyers |
Publisher | : Springer Science & Business Media |
Total Pages | : 1885 |
Release | : 2011-10-05 |
Genre | : Mathematics |
ISBN | : 1461418054 |
Download Mathematics of Complexity and Dynamical Systems Book in PDF, ePub and Kindle
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author | : Jerrold E. Marsden |
Publisher | : Springer Science & Business Media |
Total Pages | : 593 |
Release | : 2013-03-19 |
Genre | : Science |
ISBN | : 0387217924 |
Download Introduction to Mechanics and Symmetry Book in PDF, ePub and Kindle
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
Author | : Jerrold E. Marsden |
Publisher | : Cambridge University Press |
Total Pages | : 272 |
Release | : 1992-04-30 |
Genre | : Mathematics |
ISBN | : 9780521428446 |
Download Lectures on Mechanics Book in PDF, ePub and Kindle
Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.
Author | : Jerrold E. Marsden |
Publisher | : Springer |
Total Pages | : 527 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 3540724702 |
Download Hamiltonian Reduction by Stages Book in PDF, ePub and Kindle
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Author | : |
Publisher | : |
Total Pages | : 820 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews Book in PDF, ePub and Kindle
Author | : Andrei A. Agrachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2013-03-14 |
Genre | : Science |
ISBN | : 3662064049 |
Download Control Theory from the Geometric Viewpoint Book in PDF, ePub and Kindle
This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.