Synopsis
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 EulerLagrange 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, LiePoisson 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 books many examples and worked exercises make it ideal for both classroom use and self-study.
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Présentation de l'éditeur
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 EulerLagrange 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, LiePoisson 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 books many examples and worked exercises make it ideal for both classroom use and self-study.
Revue de presse
Both books are very readable; the author has an easy, informal style ... These two books, written by one of the masters in geometric mechanics, provide an accessible way into the subject for newcomers; they also give a unique perspective for those who are not so new. --Professor Peter Hydon, UK Nonlinear News Review
This two-volume book fills a niche in the geometric mechanics literature at the crossroads between mathematics and physics/engineering and between elementary and advanced texts on theoretical mechanics. --Mathematical Reviews
Students who work carefully through the material in these volumes will amass a formidable armory of mathematical techniques and will be well equipped to attack new and challenging problems in mechanics ... The appendices contain a collection of valuable example problems that are suitable for both homework and enhanced coursework. There are also numerous exercises scattered throughout the text to allow readers to evaluate their progress. --SIAM Review
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
Résultats de recherche pour Geometric Mechanics: Rotating, Translating and Rolling
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GEOMETRIC MECHANICS: Part 2, Rotating, Translating and Rolling.
Edité par
Imperial College Press., 2008
ISBN 10 : 1848161557
ISBN 13 : 9781848161559
Ancien ou d'occasion
Couverture rigide
Vendeur : Universitätsbuchhandlung Herta Hold GmbH, Berlin, Allemagne
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15 x 23 cm. 312 pages. HC Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Sprache: Englisch. N° de réf. du vendeur 7957VB
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GEOMETRIC MECHANICS, PART II: ROTATING, TRANSLATING AND ROLLING
Edité par
Imperial College Press, 2008
ISBN 10 : 1848161557
ISBN 13 : 9781848161559
Neuf
Couverture rigide
Vendeur : Basi6 International, Irving, TX, Etats-Unis
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Etat : Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service. N° de réf. du vendeur ABEOCT25-388966
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GEOMETRIC MECHANICS (PART II)
Edité par
Imperial College Press, 2008
ISBN 10 : 1848161557
ISBN 13 : 9781848161559
Neuf
Couverture rigide
Vendeur : Romtrade Corp., STERLING HEIGHTS, MI, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Etat : New. This is a Brand-new US Edition. This Item may be shipped from US or any other country as we have multiple locations worldwide. N° de réf. du vendeur ABBB-226393
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Geometric Mechanics, Part II: Rotating, Translating and Rolling
Edité par
Imperial College Press, 2008
ISBN 10 : 1848161557
ISBN 13 : 9781848161559
Ancien ou d'occasion
Couverture rigide
Vendeur : killarneybooks, Inagh, CLARE, Irlande
Évaluation du vendeur 5 sur 5 étoiles
Hardcover. Etat : Very Good. Hardcover, xvi + 294 pages, NOT ex-library. Neatly removed title page, else great shape. Book is clean and bright throughout with unmarked text, free of inscriptions and stamps, firmly bound. Issued without a dust jacket. -- Contents: Preface; 1 Galileo [Principle of Galilean relativity; Galilean transformations; Lie group actions of SE(3) & G(3)] 2 Newton, Lagrange, Hamilton [Newton (Newtonian form of free rigid rotation; Newtonian form of rigid-body motion); Lagrange (Principle of stationary action); Noether's theorem (Lie symmetries & conservation laws; Infinitesimal transformations of a Lie group); Lagrangian form of rigid-body motion (Hamilton-Pontryagin variations; Manakov's formulation of the SO(n) rigid body; Matrix Euler-Poincar'e equations; Manakov's integration of the SO(n) rigid body); Hamilton (Hamiltonian form of rigid-body motion; Lie-Poisson Hamiltonian rigid-body dynamics; Nambu's R3 Poisson bracket; Clebsch variational principle for the rigid body)] 3 Quaternions [Operating with quaternions (Quaternion multiplication using Pauli matrices; Quaternionic conjugate; Decomposition of three-vectors; Alignment dynamics for Newton's 2nd Law; Quaternionic dynamics of Kepler's problem); Quaternionic conjugation (Quaternionic conjugation in CK terms; Pure quaternions, Pauli matrices & SU(2); Tilde map: R3=su(2)=so(3); Pauli matrices and Poincare's sphere C2 to S2; Poincare's sphere and Hopf's fibration)] 4 Quaternionic conjugacy [Cayley-Klein dynamics (Cayley-Klein parameters, rigid-body dynamics; Body angular frequency; Hamilton's principle in CK parameters); Actions of quaternions] 5 Special orthogonal group [Adjoint and coadjoint actions of SO(3)] 6 Special Euclidean group [Introduction to SE(3); Adjoint operations for SE(3); Adjoint actions of se(3); Left versus Right] 7 Geometric Mechanics on SE(3) [Left-invariant Lagrangians; Kirchhoff equations] 8 Heavy top equations [Introduction and definitions; Heavy top action principle; Lie-Poisson brackets; Clebsch action principle; Kaluza-Klein construction] 9 Euler-Poincare theorem [Action principles on Lie algebras; Hamilton-Pontryagin principle; Clebsch approach to Euler-Poincare; Lie-Poisson Hamiltonian formulation] 10 Lie-Poisson Hamiltonian form [Hamiltonian continuum spin chain] 11 Momentum maps [Standard momentum map; Cotangent lift; Examples] 12 Round rolling rigid bodies [Introduction (Holonomic versus nonholonomic; Chaplygin's top); Hamilton-Pontryagin principle; Nonholonomic symmetry reduction (Semidirect-product structure; Euler-Poincare theorem)] A Geometrical structure [Manifolds; Motion: Tangent vectors and flows (Vector fields, integral curves and flows; Differentials of functions: The cotangent bundle); Tangent and cotangent lifts (Summary of derivatives on manifolds)] B Lie groups and Lie algebras [Matrix Lie groups; Defining matrix Lie algebras; Examples of matrix Lie groups; Lie group actions (Left and right translations on a Lie group); Tangent and cotangent lift actions; Jacobi-Lie bracket; Lie derivative and Jacobi-Lie bracket (Lie derivative of a vector field; Vector fields in ideal fluid dynamics)] C Enhanced coursework [Variations on rigid-body dynamics (Two times; Rotations in complex space; Rotations in four dimensions: SO(4)); C3 oscillators; GL(n, R) symmetry]; Bibliography; Index. N° de réf. du vendeur 010904
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