Download or read book Geometry of Nonholonomically Constrained Systems written by Richard H. Cushman and published by World Scientific. This book was released on 2010 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonholonomic Mechanics and Control written by A.M. Bloch and published by Springer Science & Business Media. This book was released on 2008-02-03 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
Download or read book Geometry of Nonholonomically Constrained Systems written by Richard H. Cushman and published by World Scientific. This book was released on 2010 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat. The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trail-blazers in their respective fields.
Download or read book Nonholonomic Mechanics and Control written by A.M. Bloch and published by Springer Science & Business Media. This book was released on 2007-09-27 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
Download or read book The Breadth of Symplectic and Poisson Geometry written by Jerrold E. Marsden and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: * The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics
Download or read book Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint written by Patrick J. Rabier and published by SIAM. This book was released on 2000-01-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several issues are investigated in depth to provide a sound and complete justification of the DAE model. These issues include the development of a generalized Gauss principle of least constraint, a study of the effect of the failure of an important full-rank condition, and a precise characterization of the state spaces. In particular, when the mentioned full-rank condition is not satisfied, this book shows how a new set of equivalent constraints can be constructed in a completely intrinsic way, where, in general, these new constraints comply with the full-rank requirement.
Download or read book Geometric Control and Numerical Aspects of Nonholonomic Systems written by Jorge Cortés Monforte and published by Springer. This book was released on 2004-10-19 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.
Download or read book Stochastic Geometric Mechanics written by Sergio Albeverio and published by Springer. This book was released on 2017-11-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled “Geometric mechanics – variational and stochastic methods” run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists in different areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.
Download or read book Dynamics of Nonholonomic Systems written by Juru Isaakovich Ne_mark and published by American Mathematical Soc.. This book was released on 2004-07-16 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to give a comprehensive and systematic exposition of the mechanics of nonholonomic systems, including the kinematics and dynamics of nonholonomic systems with classical nonholonomic constraints, the theory of stability of nonholonomic systems, technical problems of the directional stability of rolling systems, and the general theory of electrical machines. The book contains a large number of examples and illustrations.
Download or read book CONTROLO 2020 written by José Alexandre Gonçalves and published by Springer Nature. This book was released on 2020-09-08 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely and comprehensive snapshot of research and developments in the field of control engineering. Covering a wide range of theoretical and practical issues, the contributions describes a number of different control approaches, such adaptive control, fuzzy and neuro-fuzzy control, remote and robust control systems, real time an fault tolerant control, among others. Sensors and actuators, measurement systems, renewable energy systems, aerospace systems as well as industrial control and automation, are also comprehensively covered. Based on the proceedings of the 14th APCA International Conference on Automatic Control and Soft Computing, held on July 1-3, 2020, in Bragança, Portugal, the book offers a timely and thoroughly survey of the latest research in the field of control, and a source of inspiration for researchers and professionals worldwide.
Download or read book Geometric Aspects of Analysis and Mechanics written by Erik P. van den Ban and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields. Written in his honor, the invited and refereed articles in this volume contain important new results as well as surveys in some of these areas, clearly demonstrating the impact of Duistermaat's research and, in addition, exhibiting interrelationships among many of the topics.
Download or read book New Developments in Differential Geometry Budapest 1996 written by J. Szenthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996
Download or read book Differential Geometry of Singular Spaces and Reduction of Symmetry written by Jędrzej Śniatycki and published by Cambridge University Press. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
Download or read book IUTAM Symposium on Hamiltonian Dynamics Vortex Structures Turbulence written by Alexey V. Borisov and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.
Download or read book Non commuting Variations in Mathematics and Physics written by Serge Preston and published by Springer. This book was released on 2016-03-02 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.
Download or read book Differential Geometry and Its Applications written by Old?ich Kowalski and published by World Scientific. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture ?Leonhard Euler ? 300 years on? by R Wilson. Notable contributors include J F Cari¤ena, M Castrill¢n L¢pez, J Erichhorn, J-H Eschenburg, I Kol ?, A P Kopylov, J Korba?, O Kowalski, B Kruglikov, D Krupka, O Krupkov , R Landre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Mu¤oz Masqu, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slov k, J Szilasi, L Tam ssy, P Walczak, and others.
