Holm Darryl D's Books

Geometric Mechanics

Part II: Rotating, Translating and Rolling

By: Darryl D Holm

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Geometric Mechanics

Part II: Rotating, Translating and Rolling

By: Darryl D Holm

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.

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311

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1911299336

ISBN 13

9781911299332

Mathematics Of Planet Earth: A Primer

By: Jochen Broecker,Ben Calderhead,Davoud Cheraghi,Colin Cotter,Darryl D Holm,Tobias Kuna,Beatrice Pelloni,Ted Shepherd,Hilary Weller

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Mathematics Of Planet Earth: A Primer

By: Jochen Broecker,Ben Calderhead,Davoud Cheraghi,Colin Cotter,Darryl D Holm,Tobias Kuna,Beatrice Pelloni,Ted Shepherd,Hilary Weller

Mathematics of Planet Earth (MPE) was started and continues to be consolidated as a collaboration of mathematical science organisations around the world. These organisations work together to tackle global environmental, social and economic problems using mathematics.This textbook introduces the fundamental topics of MPE to advanced undergraduate and graduate students in mathematics, physics and engineering while explaining their modern usages and operational connections. In particular, it discusses the links between partial differential equations, data assimilation, dynamical systems, mathematical modelling and numerical simulations and applies them to insightful examples.The text also complements advanced courses in geophysical fluid dynamics (GFD) for meteorology, atmospheric science and oceanography. It links the fundamental scientific topics of GFD with their potential usage in applications of climate change and weather variability. The immediacy of examples provides an excellent introduction for experienced researchers interested in learning the scope and primary concepts of MPE.

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Page Count

371

Publisher

World Scientific

Published Date

ISBN 10

1786343851

ISBN 13

9781786343857

Crossover-Time in Quantum Boson and Spin Systems

By: Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm

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Crossover-Time in Quantum Boson and Spin Systems

By: Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm

The authors compare classical and quantum dynamics in the quasiclassical region of parameters and under the condition of unstable (chaotic) classical behavior. They estimate the characteristic time-scale at which classical and quantum solutions start to differ significantly. The method is based on exact equations for time-dependent expectation values in boson and spin coherent states, and applies to rather general Hamiltonians with many degrees of freedom. The authors develop a consistent dynamical theory for quantum nonintegrable Hamiltonians and provide explicit examples of classical-quantum "crossover-time", a very common and fundamental phenomenon in quantum nonintegrable systems. This book can be recommended to graduate students and to specialists.

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279

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540484159

ISBN 13

9783540484158

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

By: Darryl D Holm

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

By: Darryl D Holm

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

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Page Count

411

Publisher

World Scientific

Published Date

ISBN 10

1911298666

ISBN 13

9781911298663

Geometric Mechanics and Symmetry

From Finite to Infinite Dimensions

By: Darryl D. Holm,Tanya Schmah,Cristina Stoica

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Geometric Mechanics and Symmetry

From Finite to Infinite Dimensions

By: Darryl D. Holm,Tanya Schmah,Cristina Stoica

Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincaré equations for dynamics on Lie groups. Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincaré reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.

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Publisher

Oxford University Press

Published Date

ISBN 10

0191549878

ISBN 13

9780191549878

Geometric Mechanics: Dynamics and symmetry

By: Darryl D. Holm

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Geometric Mechanics: Dynamics and symmetry

By: Darryl D. Holm

Advanced undergraduate and graduate students in mathematics, physics and engineering.

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375

Publisher

Imperial College Press

Published Date

ISBN 10

1848161956

ISBN 13

9781848161955

Geometric Mechanics: Rotating, translating and rolling

By: Darryl D. Holm

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Geometric Mechanics: Rotating, translating and rolling

By: Darryl D. Holm

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.

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Page Count

311

Publisher

Imperial College Press

Published Date

ISBN 10

1848161557

ISBN 13

9781848161559

Geometric Mechanics

By: Darryl D. Holm

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Geometric Mechanics

By: Darryl D. Holm

Advanced undergraduate and graduate students in mathematics, physics and engineering.

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ISBN 10

1848167784

ISBN 13

9781848167780

Geometric Mechanics: Rotating, translating and rolling

By: Darryl D. Holm

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Geometric Mechanics: Rotating, translating and rolling

By: Darryl D. Holm

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311

Publisher

Imperial College Press

Published Date

ISBN 10

1848161557

ISBN 13

9781848161559

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

By: Darryl D Holm

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

By: Darryl D Holm

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

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466

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1911298658

ISBN 13

9781911298656

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

By: Darryl D Holm

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

By: Darryl D Holm

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466

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1911298658

ISBN 13

9781911298656

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

By: Darryl D Holm

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

By: Darryl D Holm

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411

Publisher

World Scientific

Published Date

ISBN 10

1911298666

ISBN 13

9781911298663

Geometric Mechanics and Symmetry

From Finite to Infinite Dimensions

By: Darryl D. Holm,Tanya Schmah,Cristina Stoica

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Geometric Mechanics and Symmetry

From Finite to Infinite Dimensions

By: Darryl D. Holm,Tanya Schmah,Cristina Stoica

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.

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537

Publisher

Oxford University Press

Published Date

ISBN 10

0199212902

ISBN 13

9780199212903

Geometric Mechanics: Dynamics and symmetry

By: Darryl D. Holm

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Geometric Mechanics: Dynamics and symmetry

By: Darryl D. Holm

Advanced undergraduate and graduate students in mathematics, physics and engineering.

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Page Count

375

Publisher

Imperial College Press

Published Date

ISBN 10

1848161956

ISBN 13

9781848161955

Crossover-Time in Quantum Boson and Spin Systems

By: Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm

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Crossover-Time in Quantum Boson and Spin Systems

By: Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm

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Solve jigsaw puzzle

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Page Count

279

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540484159

ISBN 13

9783540484158

Book's by Holm Darryl D

Geometric Mechanics

Geometric Mechanics

Mathematics Of Planet Earth: A Primer

Mathematics Of Planet Earth: A Primer

Crossover-Time in Quantum Boson and Spin Systems

Crossover-Time in Quantum Boson and Spin Systems

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

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

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry

Geometric Mechanics: Dynamics and symmetry

Geometric Mechanics: Dynamics and symmetry

Geometric Mechanics: Rotating, translating and rolling

Geometric Mechanics: Rotating, translating and rolling

Geometric Mechanics

Geometric Mechanics

Geometric Mechanics: Rotating, translating and rolling

Geometric Mechanics: Rotating, translating and rolling

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

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

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

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

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

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

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry

Geometric Mechanics: Dynamics and symmetry

Geometric Mechanics: Dynamics and symmetry

Crossover-Time in Quantum Boson and Spin Systems

Crossover-Time in Quantum Boson and Spin Systems

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