Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition
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Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition
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Author : Holm Darryl D
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-07-13
Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition written by Holm Darryl D and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-13 with Mathematics categories.
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
Geometric Mechanics Dynamics And Symmetry
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Author : Darryl D. Holm
language : en
Publisher: Imperial College Press
Release Date : 2008-01-01
Geometric Mechanics Dynamics And Symmetry 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 2008-01-01 with Mathematics categories.
Advanced undergraduate and graduate students in mathematics, physics and engineering.
Geometric Mechanics Part Ii Rotating Translating And Rolling 2nd Edition
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Author : Holm Darryl D
language : en
Publisher: World Scientific
Release Date : 2011-10-31
Geometric Mechanics Part Ii Rotating Translating And Rolling 2nd Edition written by Holm Darryl D 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
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.
Geometric Mechanics
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Author : Darryl D Holm
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-04-14
Geometric Mechanics written by Darryl D Holm and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-14 with Mathematics categories.
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
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Author : Darryl D. Holm
language : en
Publisher:
Release Date : 2011
Geometric Mechanics 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 2011 with Geometry, Differential categories.
Advanced undergraduate and graduate students in mathematics, physics and engineering.
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.
Peyresq Lectures On Geometric Mechanics And Symmetry
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Author : James Montaldi
language : en
Publisher:
Release Date : 2005
Peyresq Lectures On Geometric Mechanics And Symmetry written by James Montaldi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Introduction To Mechanics And Symmetry
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Author : Jerrold E. Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Introduction To Mechanics And Symmetry written by Jerrold E. Marsden 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 2013-03-19 with Science categories.
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.
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.