Articles liés à Geometric Mechanics: Dynamics and Symmetry

Geometric Mechanics: Dynamics and Symmetry - Couverture souple

Holm, Darryl D.

 
9781848161962: Geometric Mechanics: Dynamics and Symmetry
Couverture souple
ISBN 10 : 1848161964 ISBN 13 : 9781848161962
Editeur : Imperial College Press, 2008

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 ray optics, resonant oscillators and the elastic spherical pendulum from a unified geometric viewpoint, by formulating their solutions using reduction by Lie-group symmetries. The only prerequisites are linear algebra, calculus and some familiarity with the EulerLagrange variational principles 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 LiePoisson Hamiltonian formulations and momentum maps in physical applications. The many Exercises and Worked Answers aid 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 book's many worked exercises make it ideal for both classroom use and self-study. In particular, a substantial appendix containing both introductory examples and enhanced coursework problems with worked answers is included to help the student develop proficiency in using the powerful methods of geometric mechanics.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

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 ray optics, resonant oscillators and the elastic spherical pendulum from a unified geometric viewpoint, by formulating their solutions using reduction by Lie-group symmetries. The only prerequisites are linear algebra, calculus and some familiarity with the EulerLagrange variational principles 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 LiePoisson Hamiltonian formulations and momentum maps in physical applications. The many Exercises and Worked Answers aid 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 book's many worked exercises make it ideal for both classroom use and self-study. In particular, a substantial appendix containing both introductory examples and enhanced coursework problems with worked answers is included to help the student develop proficiency in using the powerful methods of geometric mechanics.

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

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

... a highly original and beautifully written account of the principles of mechanics from an advanced, unified, geometric viewpoint, using Lie-group symmetries as the perfect method for applying Poincaré's geometric approach. --Quarterly of Applied Mathematics

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Imperial College Press
Date d'édition
2008
Langue
anglais
ISBN 10 
1848161964
ISBN 13 
9781848161962
Reliure
Broché
Nombre de pages
354
Coordonnées du fabricant
non disponible
Personne responsable
gpsr@libri.de
gpsr@libri.de

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