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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 Euler-Lagrange 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 Lie-Poisson 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.

This series provides an insight into the knowledge you require to facilitate learning occuring in outdoor environments, taking the natural elements as a guide. A combination of children's voices and progression points share the approach of teaching and learning, which in 2011 received three accolades and was described as 'inspirational and sector leading'. Simple, clear and easy to use for anyone working with children from 3 - 11 years old outside. Both practical and academic guidance on the acitivity of Wood Whittling. Lutz's commonsense lessons, combined with a generous helping of fascinating anecdotes, will inspire readers in any industry. From the zesty "Garden of Eden Salad" to the "Honey Coriander Geometric Mechanics: Dynamics and Symmetry Pt. I download epub Manna Bread," each recipe will delight the palate and spark the mind. Deftly combining the sacred and the profane--the unmistakable hallmark of her fiction over the past decade--Susan Howatch gives us a spellbinding, suspenseful and psychologically intense new novel.

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Author: Darryl D. Holm
Number of Pages: 380 pages
Published Date: 01 Jun 2008
Publisher: Imperial College Press
Publication Country: London, United Kingdom
Language: English
ISBN: 9781848161962
Download Link: Click Here
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