Author: Darryl D. Holm Publisher: Imperial College Press ISBN: 1848161557 Category : Science Languages : en Pages : 311
Book Description
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.
Author: Holm Darryl D Publisher: World Scientific ISBN: 1911298666 Category : Mathematics Languages : en Pages : 412
Book Description
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
Author: Darryl D Holm Publisher: World Scientific Publishing Company ISBN: 1911299336 Category : Mathematics Languages : en Pages : 311
Book Description
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.
Author: Holm Darryl D Publisher: World Scientific Publishing Company ISBN: 1911298658 Category : Mathematics Languages : en Pages : 468
Book Description
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
Author: Lyndon O. Barton Publisher: CRC Press ISBN: 9780824787943 Category : Technology & Engineering Languages : en Pages : 744
Book Description
This updated and enlarged Second Edition provides in-depth, progressive studies of kinematic mechanisms and offers novel, simplified methods of solving typical problems that arise in mechanisms synthesis and analysis - concentrating on the use of algebra and trigonometry and minimizing the need for calculus.;It continues to furnish complete coverage of: key concepts, including kinematic terminology, uniformly accelerated motion, and the properties of vectors; graphical techniques for both velocity and acceleration analysis; analytical techniques; and ready-to-use computer and calculator programmes for analyzing basic classes of mechanisms.;This edition supplies detailed explications of such new topics as: gears, gear trains, and cams; velocity and acceleration analyses of rolling elements; acceleration analysis of sliding contact mechanisms by the effective component method; four-bar analysis by the parallelogram method; and centre of curvature determination methods.
Author: Darryl D. Holm Publisher: Oxford University Press ISBN: 0199212902 Category : Mathematics Languages : en Pages : 537
Book Description
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.
Author: Publisher: John Wiley & Sons ISBN: 1119798582 Category : Languages : en Pages :
Author: Paul A. Tipler Publisher: Macmillan ISBN: 9780716738213 Category : Science Languages : en Pages : 1342
Book Description
For nearly 25 years, Tipler’s standard-setting textbook has been a favorite for the calculus-based introductory physics course. With this edition, the book makes a dramatic re-emergence, adding innovative pedagogy that eases the learning process without compromising the integrity of Tipler’s presentation of the science. For instructor and student convenience, the Fourth Edition of Physics for Scientists and Engineers is available as three paperback volumes… Vol. 1: Mechanics, Oscillations and Waves, Thermodynamics, 768 pages, 1-57259-491-8 Vol. 2: Electricity and Magnetism, 544 pages, 1-57259-492-6 Vol. 3: Modern Physics: Quantum Mechanics, Relativity, and The Structure of Matter, 304 pages, 1-57259-490-X …or in two hardcover versions: Regular Version (Chaps. 1-35 and 39): 0-7167-3821-X Extended Version (Chaps. 1-41): 0-7167-3822-8 To order the volume or version you need, use the links above to go to each volume or version's specific page. Download errata for this book: This errata is for the first printing of Tipler's PSE, 4/e. The errors have been corrected in subsequent printings of the book, but we continue to make this errata available for those students and teachers still using old copies from the first printing. Download as a Microsoft Word document or as a pdf file.
Author: Darryl D. Holm
Author: Holm Darryl D
Author: Darryl D Holm
Author: Darryl D. Holm
Author: Kevin M. Lynch
Author: Holm Darryl D
Author: Lyndon O. Barton
Author: Darryl D. Holm
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Author: Paul A. Tipler