Geometric Mechanics Rotating Translating And Rolling

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Geometric Mechanics: Rotating, translating and rolling

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Author : Darryl D. Holm
Publisher : Imperial College Press
ISBN 13 : 1848161557
Total Pages : 311 pages
Book Rating : 4.8/5 (481 download)

Book Synopsis Geometric Mechanics: Rotating, translating and rolling by : Darryl D. Holm

Download or read book Geometric Mechanics: Rotating, translating and rolling written by Darryl D. Holm and published by Imperial College Press. This book was released on 2008 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Mechanics

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Author : Darryl D Holm
Publisher : World Scientific Publishing Company
ISBN 13 : 1911299336
Total Pages : 311 pages
Book Rating : 4.9/5 (112 download)

Book Synopsis Geometric Mechanics by : Darryl D Holm

Download or read book Geometric Mechanics written by Darryl D Holm and published by World Scientific Publishing Company. This book was released on 2008-04-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. It 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. 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. Variational calculus on tangent spaces of Lie groups is explained in the context of familiar concrete examples. 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, and 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 120 Exercises and 55 Worked Answers help the student to grasp the essential aspects of the subject, and to develop proficiency in using the powerful methods of geometric mechanics. In addition, all theorems are stated and proved explicitly. The book's many examples and worked exercises make it ideal for both classroom use and self-study. Contents: GalileoNewton, Lagrange, HamiltonQuaternionsQuaternionic ConjugacySpecial Orthogonal GroupThe Special Euclidean GroupGeometric Mechanics on SE(3)Heavy Top EquationsThe Euler–Poincaré TheoremLie–Poisson Hamiltonian FormMomentum MapsRound Rolling Rigid Bodies Readership: Advanced undergraduate and graduate students in mathematics, physics and engineering; researchers interested in learning the basic ideas in the fields; non-experts interested in geometric mechanics, dynamics and symmetry.

Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition)

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Author : Holm Darryl D
Publisher : World Scientific
ISBN 13 : 1911298666
Total Pages : 412 pages
Book Rating : 4.9/5 (112 download)

Book Synopsis Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) by : Holm Darryl D

Download or read book Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) written by Holm Darryl D and published by World Scientific. This book was released on 2011-10-31 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition)

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Author : Holm Darryl D
Publisher : World Scientific Publishing Company
ISBN 13 : 1911298658
Total Pages : 468 pages
Book Rating : 4.9/5 (112 download)

Book Synopsis Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) by : Holm Darryl D

Download or read book Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) written by Holm Darryl D and published by World Scientific Publishing Company. This book was released on 2011-07-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: See also GEOMETRIC MECHANICS — Part II: Rotating, Translating and Rolling (2nd Edition) This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton's principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.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. In particular, the role of Noether's theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications./a

Rotating, translating and rolling

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Author : Darryl D. Holm
Publisher :
ISBN 13 : 9781848161559
Total Pages : pages
Book Rating : 4.1/5 (615 download)

Book Synopsis Rotating, translating and rolling by : Darryl D. Holm

Download or read book Rotating, translating and rolling written by Darryl D. Holm and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and graduate students in mathematics, physics and engineering.

Geometric Mechanics: Rotating, translating and rolling

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Author : Darryl D. Holm
Publisher :
ISBN 13 : 9781848161566
Total Pages : 294 pages
Book Rating : 4.1/5 (615 download)

Book Synopsis Geometric Mechanics: Rotating, translating and rolling by : Darryl D. Holm

Download or read book Geometric Mechanics: Rotating, translating and rolling written by Darryl D. Holm and published by . This book was released on 2008 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. It 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. 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.

Dynamical Systems and Geometric Mechanics

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Author : Jared Maruskin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110597802
Total Pages : 348 pages
Book Rating : 4.1/5 (15 download)

Book Synopsis Dynamical Systems and Geometric Mechanics by : Jared Maruskin

Download or read book Dynamical Systems and Geometric Mechanics written by Jared Maruskin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Geometric Mechanics and Symmetry

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Author : Darryl D. Holm
Publisher : Oxford University Press
ISBN 13 : 0199212902
Total Pages : 537 pages
Book Rating : 4.1/5 (992 download)

Book Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm

Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.

Differential Geometrical Theory of Statistics

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Author : Frédéric Barbaresco
Publisher : MDPI
ISBN 13 : 3038424242
Total Pages : 473 pages
Book Rating : 4.0/5 (384 download)

Book Synopsis Differential Geometrical Theory of Statistics by : Frédéric Barbaresco

Download or read book Differential Geometrical Theory of Statistics written by Frédéric Barbaresco and published by MDPI. This book was released on 2018-04-06 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy

Lie Groups, Differential Equations, and Geometry

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Author : Giovanni Falcone
Publisher : Springer
ISBN 13 : 3319621815
Total Pages : 361 pages
Book Rating : 4.3/5 (196 download)

Book Synopsis Lie Groups, Differential Equations, and Geometry by : Giovanni Falcone

Download or read book Lie Groups, Differential Equations, and Geometry written by Giovanni Falcone and published by Springer. This book was released on 2017-09-19 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

A Visual Introduction to Differential Forms and Calculus on Manifolds

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Author : Jon Pierre Fortney
Publisher : Springer
ISBN 13 : 3319969927
Total Pages : 468 pages
Book Rating : 4.3/5 (199 download)

Book Synopsis A Visual Introduction to Differential Forms and Calculus on Manifolds by : Jon Pierre Fortney

Download or read book A Visual Introduction to Differential Forms and Calculus on Manifolds written by Jon Pierre Fortney and published by Springer. This book was released on 2018-11-03 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

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Author : Taeyoung Lee
Publisher : Springer
ISBN 13 : 3319569538
Total Pages : 539 pages
Book Rating : 4.3/5 (195 download)

Book Synopsis Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by : Taeyoung Lee

Download or read book Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds written by Taeyoung Lee and published by Springer. This book was released on 2017-08-14 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Mathematical Modelling of Physical Systems

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Author : Michel Cessenat
Publisher : Springer
ISBN 13 : 3319947583
Total Pages : 505 pages
Book Rating : 4.3/5 (199 download)

Book Synopsis Mathematical Modelling of Physical Systems by : Michel Cessenat

Download or read book Mathematical Modelling of Physical Systems written by Michel Cessenat and published by Springer. This book was released on 2018-10-26 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is placed on specifying the agreement between the functional framework and its physical necessity and on making clear the intrinsic character of physical elements, independent from specific charts or frames. The book is divided into four sections, covering thermostructure, classical mechanics, fluid mechanics modelling, and behavior laws. An extensive appendix provides notations and definitions as well as brief explanation of integral manifolds, symplectic structure, and contact structure. Plenty of examples are provided throughout the book, and reviews of basic principles in differential geometry and convex analysis are presented as needed. This book is a useful resource for graduate students and researchers in the field.

Geometric Science of Information

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Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3642400205
Total Pages : 863 pages
Book Rating : 4.6/5 (424 download)

Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2013-08-19 with total page 863 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.

Theoretical Foundations of Nanoscale Quantum Devices

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Author : Malin Premaratne
Publisher : Cambridge University Press
ISBN 13 : 1108639364
Total Pages : 299 pages
Book Rating : 4.1/5 (86 download)

Book Synopsis Theoretical Foundations of Nanoscale Quantum Devices by : Malin Premaratne

Download or read book Theoretical Foundations of Nanoscale Quantum Devices written by Malin Premaratne and published by Cambridge University Press. This book was released on 2021-01-07 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanooptics which describes the interaction of light with matter at the nanoscale, is a topic of great fundamental interest to physicists and engineers and allows the direct observation of quantum mechanical phenomena in action. This self-contained and extensively referenced text describes the underlying theory behind nanodevices operating in the quantum regime for use both in advanced courses and as a reference for researchers in physics, chemistry, electrical engineering, and materials science. Presenting an extensive theoretical toolset for design and analysis of nanodevices, the authors demonstrate the art of developing approximate quantum models of real nanodevices. The rudimentary mathematical knowledge required to master the material is carefully introduced, with detailed derivations and frequent worked examples allowing readers to gain a thorough understanding of the material. More advanced applications are gradually introduced alongside analytical approximations and simplifying assumptions often used to make such problems tractable while representative of the observed features.

Linear Algebra and Group Theory for Physicists and Engineers

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Author : Yair Shapira
Publisher : Springer Nature
ISBN 13 : 3031224221
Total Pages : 583 pages
Book Rating : 4.0/5 (312 download)

Book Synopsis Linear Algebra and Group Theory for Physicists and Engineers by : Yair Shapira

Download or read book Linear Algebra and Group Theory for Physicists and Engineers written by Yair Shapira and published by Springer Nature. This book was released on 2023-01-16 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity. This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained—readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline. The second edition has been revised and updated throughout and includes new material on the Jordan form, the Hermitian matrix and its eigenbasis, and applications in numerical relativity and electromagnetics.

Geometry of Submanifolds and Applications

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Author : Bang-Yen Chen
Publisher : Springer Nature
ISBN 13 : 981999750X
Total Pages : 230 pages
Book Rating : 4.8/5 (199 download)

Book Synopsis Geometry of Submanifolds and Applications by : Bang-Yen Chen

Download or read book Geometry of Submanifolds and Applications written by Bang-Yen Chen and published by Springer Nature. This book was released on with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: