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Book review: Geometric mechanics

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  • The first Part of the two Geometric Mechanics books focuses on dynamics in geometric mechanical systems and using Lie symmetry reductions to analyse the dynamics. The second Part looks in depth at translational and rotational motions of rigid bodies in the geometric context of Lie symmetry groups and sets up the Euler-Poincare framework. It finishes with a chapter on rolling motion as an example of applications of the framework to other problems in geometric mechanics. The aim of the Geometric Mechanics books is to make the reader familiar with the concepts of geometric mechanics and the power of symmetry reduction. Mathematical rigour is not an aim, though details of the proofs of most statements in Part I are provided. As pointed out in its preface, Part II has a more inquiry based approach and doesn't focus on mathematical rigour. Instead many references are given and there are two appendices providing more mathematical background. In both Parts, physical examples play an important role. Indeed, all concepts and theory are motivated by examples. There are also excellent references to recent literature as well as nice historic contexts. The level of the books is aimed at advanced undergraduate students and beginning graduate students. The assumed background consists of first courses in classical mechanics, standard linear algebra, vector calculus and ordinary differential equations. No knowledge of differential geometry or Lie groups is assumed, these topics are introduced when needed in the books.

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