Download E-books Geometric Mechanics - Part I: Dynamics and Symmetry (2nd Edition) PDF

This textbook introduces the instruments and language of contemporary geometric mechanics to complicated undergraduates and starting graduate scholars in arithmetic, physics and engineering. It treats the elemental difficulties of dynamical structures from the perspective of Lie crew symmetry in variational rules. the one must haves are linear algebra, calculus and a few familiarity with Hamilton's precept and canonical Poisson brackets in classical mechanics firstly undergraduate point.

the information and ideas of geometric mechanics are defined within the context of particular examples. via those examples, the scholar develops abilities in acting computational manipulations, ranging from Fermat's precept, operating during the concept of differential varieties on manifolds and moving those rules to the purposes of aid via symmetry to bare Lie-Poisson Hamiltonian formulations and momentum maps in actual functions.

the numerous routines and labored solutions within the textual content permit the scholar to know the basic features of the topic. moreover, the fashionable language and alertness of differential kinds is defined within the context of geometric mechanics, in order that the significance of Lie derivatives and their flows is apparent. All theorems are said and proved explicitly.

The enterprise of the 1st version has been preserved within the moment version. in spite of the fact that, the substance of the textual content has been rewritten all through to enhance the move and to counterpoint the improvement of the fabric. specifically, the position of Noether's theorem concerning the implications of Lie team symmetries for conservation legislation of dynamical structures has been emphasized all through, with many applications.

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