Geometry Of Constrained Dynamical Systems

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Geometry Of Constrained Dynamical Systems

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Author : John M. Charap
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-05

Geometry Of Constrained Dynamical Systems written by John M. Charap and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-05 with Mathematics categories.

A lively, varied and topical presentation of this branch of theoretical physics.

Geometry Of Nonholonomically Constrained Systems

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Author : Richard H. Cushman
language : en
Publisher: World Scientific
Release Date : 2010

Geometry Of Nonholonomically Constrained Systems written by Richard H. Cushman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

1. Nonholonomically constrained motions. 1.1. Newton's equations. 1.2. Constraints. 1.3. Lagrange-d'Alembert equations. 1.4. Lagrange derivative. 1.5. Hamilton-d'Alembert equations. 1.6. Distributional Hamiltonian formulation. 1.7. Almost Poisson brackets. 1.8. Momenta and momentum equation. 1.9. Projection principle. 1.10. Accessible sets. 1.11. Constants of motion. 1.12. Notes -- 2. Group actions and orbit spaces. 2.1. Group actions. 2.2. Orbit spaces. 2.3. Isotropy and orbit types. 2.4. Smooth structure on an orbit space. 2.5. Subcartesian spaces. 2.6. Stratification of the orbit space by orbit types. 2.7. Derivations and vector fields on a differential space. 2.8. Vector fields on a stratified differential space. 2.9. Vector fields on an orbit space. 2.10. Tangent objects to an orbit space. 2.11. Notes -- 3. Symmetry and reduction. 3.1. Dynamical systems with symmetry. 3.2. Nonholonomic singular reduction. 3.3. Nonholonomic regular reduction. 3.4. Chaplygin systems. 3.5. Orbit types and reduction. 3.6. Conservation laws. 3.7. Lifted actions and the momentum equation. 3.8. Notes -- 4. Reconstruction, relative equilibria and relative periodic orbits. 4.1. Reconstruction. 4.2. Relative equilibria. 4.3. Relative periodic orbits. 4.4. Notes -- 5. Carathéodory's sleigh. 5.1. Basic set up. 5.2. Equations of motion. 5.3. Reduction of the E(2) symmetry. 5.4. Motion on the E(2) reduced phase space. 5.5. Reconstruction. 5.6. Notes -- 6. Convex rolling rigid body. 6.1. Basic set up. 6.2. Unconstrained motion. 6.3. Constraint distribution. 6.4. Constrained equations of motion. 6.5. Reduction of the translational [symbol] symmetry. 6.6. Reduction of E(2) symmetry. 6.7. Body of revolution. 6.8. Notes -- 7. The rolling disk. 7.1. General set up. 7.2. Reduction of the E(2) x S[symbol] symmetry. 7.3. Reconstruction. 7.4. Relative equilibria. 7.5. A potential function on an interval. 7.6. Scaling. 7.7. Solutions of the rescaled Chaplygin equations. 7.8. Bifurcations of a vertical disk. 7.9. The global geometry of the degeneracy locus. 7.10. Falling flat. 7.11. Near falling flat. 7.12. The bifurcation diagram. 7.13. The integral map. 7.14. Constant energy slices. 7.15. The spatial rotational shift. 7.16. Notes.

Classical And Quantum Dynamics Of Constrained Hamiltonian Systems

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Author : Heinz J. Rothe
language : en
Publisher: World Scientific
Release Date : 2010

Classical And Quantum Dynamics Of Constrained Hamiltonian Systems written by Heinz J. Rothe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.

Handbook Of Geometric Constraint Systems Principles

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Author : Meera Sitharam
language : en
Publisher: CRC Press
Release Date : 2018-07-20

Handbook Of Geometric Constraint Systems Principles written by Meera Sitharam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-20 with Mathematics categories.

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds

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Author : A.K. Prykarpatsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09

Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds written by A.K. Prykarpatsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

A Practical Approach To Dynamical Systems For Engineers

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Author : Patricia Mellodge
language : en
Publisher: Woodhead Publishing
Release Date : 2015-11-19

A Practical Approach To Dynamical Systems For Engineers written by Patricia Mellodge and has been published by Woodhead Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Mathematics categories.

A Practical Approach to Dynamical Systems for Engineers takes the abstract mathematical concepts behind dynamical systems and applies them to real-world systems, such as a car traveling down the road, the ripples caused by throwing a pebble into a pond, and a clock pendulum swinging back and forth. Many relevant topics are covered, including modeling systems using differential equations, transfer functions, state-space representation, Hamiltonian systems, stability and equilibrium, and nonlinear system characteristics with examples including chaos, bifurcation, and limit cycles. In addition, MATLAB is used extensively to show how the analysis methods are applied to the examples. It is assumed readers will have an understanding of calculus, differential equations, linear algebra, and an interest in mechanical and electrical dynamical systems. - Presents applications in engineering to show the adoption of dynamical system analytical methods - Provides examples on the dynamics of automobiles, aircraft, and human balance, among others, with an emphasis on physical engineering systems - MATLAB and Simulink are used throughout to apply the analysis methods and illustrate the ideas - Offers in-depth discussions of every abstract concept, described in an intuitive manner, and illustrated using practical examples, bridging the gap between theory and practice - Ideal resource for practicing engineers who need to understand background theory and how to apply it

Geometry Of Constrained Dynamical System

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Author :
language : en
Publisher:
Release Date : 1995

Geometry Of Constrained Dynamical System written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Geometric Mechanics Rotating Translating And Rolling

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Author : Darryl D. Holm
language : en
Publisher: Imperial College Press
Release Date : 2008

Geometric Mechanics Rotating Translating And Rolling written by Darryl D. Holm and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

Introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. This book treats the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint, by formulating their solutions as coadjoint motions generated by Lie groups.

Icgg 2022 Proceedings Of The 20th International Conference On Geometry And Graphics

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Author : Liang-Yee Cheng
language : en
Publisher: Springer Nature
Release Date : 2022-08-12

Icgg 2022 Proceedings Of The 20th International Conference On Geometry And Graphics written by Liang-Yee Cheng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-12 with Technology & Engineering categories.

This book covers recent achievements on the ever-expanding field of Geometry and Graphics on both analogical and digital fronts, from theoretical investigations to a broad range of applications, new teaching methodologies, and historical aspects. It is from 20th International Conference on Geometry and Graphics (ICGG2022), a series of conference that started in 1978 and promoted by International Society for Geometry and Graphics, which aims to foster international collaboration and stimulate the scientific research and teaching innovations in the multidisciplinary field. The contents of the book are organized in: Theoretical Geometry and Graphics; Applied Geometry and Graphics; Engineering Computer Graphics; Graphics Education; Geometry and Graphics in History, and are intent for the academics, researchers, and professionals in architecture, engineering, industrial design, mathematics, and arts.

Geometric Mechanics Part Ii Rotating Translating And Rolling 2nd Edition

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Author : Darryl D Holm
language : en
Publisher: World Scientific
Release Date : 2011-10-31

Geometric Mechanics Part Ii Rotating Translating And Rolling 2nd Edition written by Darryl D Holm and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-31 with Mathematics categories.

See also GEOMETRIC MECHANICS — Part I: Dynamics and Symmetry (2nd Edition) This textbook introduces modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. In particular, it explains the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint by formulating their solutions as coadjoint motions generated by Lie groups. The only prerequisites are linear algebra, multivariable calculus and some familiarity with Euler-Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The book uses familiar concrete examples to explain variational calculus on tangent spaces of Lie groups. Through these examples, the student develops skills in performing computational manipulations, starting from vectors and matrices, working through the theory of quaternions to understand rotations, then transferring these skills to the computation of more abstract adjoint and coadjoint motions, Lie-Poisson Hamiltonian formulations, momentum maps and finally dynamics with nonholonomic constraints.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. Many worked examples of adjoint and coadjoint actions of Lie groups on smooth manifolds have also been added and the enhanced coursework examples have been expanded. The second edition is ideal for classroom use, student projects and self-study./a