This textbook introduces modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. In particular, it explains 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. The book uses familiar concrete examples to explain variational calculus on tangent spaces of Lie groups. 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, 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 organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. Many worked examples of adjoint and coadjoint actions of Lie groups on smooth manifolds have also been added and the enhanced coursework examples have been expanded. The second edition is ideal for classroom use, student projects and self-study. Key Features: • This edition preserves the organization of the first edition but the text has been rewritten throughout to improve the flow and to enrich the development of the material • The topics are presented in a straightforward style, usually by answering sequences of connected questions in the context of compelling examples, and then introducing the more advanced concepts that are revealed by these answers. This approach motivates the more abstract theory by allowing its most interesting applications to reveal its key concepts • Comprises new improvements on existing topics such as: further development of the Galilean group and the implications of Galilean relativity for Noether’s theorem; added emphasis of the role of Noether’s theorem with various applications; further development of the Manakov’s approach regarding the rigid body as an isospectral eigenvalue problem; etc • Contains additional examples of adjoint and coadjoint actions of Lie groups; additional examples of the application of Manakov’s approach; etc • Covers extra topics such as coquaternions • Includes new and enhanced coursework • There are 120 Exercises and 55 Worked Answers

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