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Abstract
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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