See also GEOMETRIC MECHANICS - Part I: Dynamics and Symmetry (2nd Edition) 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.
By:
Darryl D Holm (Imperial College London Uk)
Imprint: Imperial College Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions:
Height: 226mm,
Width: 150mm,
Spine: 18mm
Weight: 640g
ISBN: 9781848167780
ISBN 10: 1848167784
Pages: 412
Publication Date: 02 November 2011
Audience:
College/higher education
,
Further / Higher Education
Format: Paperback
Publisher's Status: Active
Galilean Relativity; Reviews of the Contributions of Newton Lagrange, Euler, Hamilton, Lie, Noether and Poincare in the Foundations of Geometric Mechanics; Rotations, Using Quaternions and Their Adjoint and Coadjoint Operations; Special Orthogonal and Special Euclidean Groups; Heavy Tops; Euler-Poincare Equations; Lie-Poisson Hamiltonian Form; Momentum Maps; Round Rolling Bodies.
Reviews for Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition)
"These volumes are a valuable addition to the literature on geometric mechanics. They are very well written, can be used for various courses independently or in conjunction with other texts, both more elementary and advanced, and can also serve as a good starting point for someone interested in the subject and willing to learn the principles and techniques of geometric mechanics. -- MathSciNet ""MathSciNet"""
