Geometric Mechanics Rotating Translating And Rolling
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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.
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
Rotating Translating And Rolling
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Author : Darryl D. Holm
language : en
Publisher:
Release Date : 2008
Rotating Translating And Rolling written by Darryl D. Holm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Advanced undergraduate and graduate students in mathematics, physics and engineering.
Dynamical Systems And Geometric Mechanics
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Author : Jared Maruskin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-21
Dynamical Systems And Geometric Mechanics written by Jared Maruskin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Science categories.
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
language : en
Publisher: Oxford University Press
Release Date : 2009-07-30
Geometric Mechanics And Symmetry written by Darryl D. Holm and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
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.
Stochastic Geometric Mechanics
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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 2017-11-17
Stochastic Geometric Mechanics written by Sergio Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Mathematics categories.
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.
Differential Geometrical Theory Of Statistics
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Author : Frédéric Barbaresco
language : en
Publisher: MDPI
Release Date : 2018-04-06
Differential Geometrical Theory Of Statistics written by Frédéric Barbaresco and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-06 with Computers categories.
This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
A Visual Introduction To Differential Forms And Calculus On Manifolds
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Author : Jon Pierre Fortney
language : en
Publisher: Springer
Release Date : 2018-11-03
A Visual Introduction To Differential Forms And Calculus On Manifolds written by Jon Pierre Fortney and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
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
language : en
Publisher: Springer
Release Date : 2017-08-14
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
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.
Linear Algebra And Group Theory For Physicists And Engineers
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Author : Yair Shapira
language : en
Publisher: Springer Nature
Release Date : 2023-01-16
Linear Algebra And Group Theory For Physicists And Engineers written by Yair Shapira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-16 with Mathematics categories.
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.