Geometric Mechanics: Rotating, Translating and Rolling - Couverture rigide

Holm, Darryl D

Couverture rigide

ISBN 10 : 1848167776 ISBN 13 : 9781848167773

Editeur : Imperial College Press, 2011

Synopsis

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A propos du livre

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 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.

Revue de presse :

"These volumes are a valuable addition to the literature on geometric mechanics. They are very well written, can be used for various courses independently or in conjunction with other texts, both more elementary and advanced, and can also serve as a good starting point for someone interested in the subject and willing to learn the principles and techniques of geometric mechanics." --MathSciNet

À propos de cette édition

• Éditeur: Imperial College Press
• Date d'édition: 2011
• ISBN 10: 1848167776
• ISBN 13: 9781848167773
• Reliure: Relié
• Numéro d'édition: 2
• Nombre de pages: 412