Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) by Darryl D Holm

Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) by Darryl D Holm

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.

Darryl D. Holm spent thirty four years at Los Alamos National Laboratory before moving in 2005 to Imperial College London as Professor of Applied Mathematics. During his career, Darryl developed a wide range of applications of the geometric approach to dynamical systems. His main interest is in
deriving and analyzing nonlinear evolution equations for multiscale phenomena. Applications of these equations have ranged from nonlinear optical pulses used in telecommunications, to turbulence modeling for global ocean circulation and climate prediction, to template matching for the shapes of
biomedical images, to directed self-assembly in nanoscience. The solution behavior of these equations includes solitons (governed by the Camassa-Holm equation), vortices and turbulence (modelled by the LANS-alpha equation) and emergent singularities (modelled by the EPDiff equation) representing the
sharp edges that appear in biomedical images.

Tanya Schmah completed her PhD in mathematics in 2001 at the Swiss Federal Institute of Technology in Lausanne. She has held lectureships at the University of Warwick (U.K.) and Macquarie University (Australia), and is currently working in the Department of Computer Science at the University of
Toronto. She has a wide range of interests in mathematics and computer science, including symmetric Hamiltonian systems and machine learning.

Cristina Stoica has a Diploma in Mathematics-Mechanics from the University of Bucharest (1991) and possesses a Doctor of Sciences degree in Astronomy awarded by the Astronomical Institute of the Romanian Academy (1997). She also holds a PhD in Applied Mathematics from the University of Victoria,
Canada (2000). Currently she is a faculty member at Wilfrid Laurier University, Canada. Her main interests lie at the intersection of dynamical systems and mathematical physics.

SKU	Unavailable
ISBN 13	9781848167780
ISBN 10	1848167784
Title	Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition)
Author	Darryl D Holm
Condition	Unavailable
Binding Type	Paperback
Publisher	Imperial College Press
Year published	2011-11-02
Number of pages	412
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.