Taeyoung Lee, Melvin Leok, N. Harris Mcclamroch

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds (eBook, PDF)

A Geometric Approach to Modeling and Analysis

• Format: PDF

Produktbeschreibung

Accessible to a broad audience of scientists and engineers

Non-trivial applications worked out in detail, allowing reader to easily apply techniques to real-world problems

Includes exercises at the end of every chapter

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 539
• Erscheinungstermin: 14. August 2017
• Englisch
• ISBN-13: 9783319569536
• Artikelnr.: 52940298

Inhaltsangabe

Mathematical Background.- Kinematics.- Classical Lagrangian and Hamiltonian Dynamics.- Langrangian and Hamiltonian Dynamics on (S1)n.- Lagrangian and Hamiltonian Dynamics on (S2)n.- Lagrangian and Hamiltonian Dynamics on SO(3).- Lagrangian and Hamiltonian Dynamics on SE(3).- Lagrangian and Hamiltonian Dynamics on Manifolds.- Rigid and Mult-body Systems.- Deformable Multi-body Systems.- Fundamental Lemmas of the Calculus of Variations.- Linearization as an Approximation to Lagrangian Dynamics on a Manifold.

Rezensionen

"This book presents a monograph on foundational geometric principles of Lagrangian and Hamiltonian dynamics and their application in studying important physical systems. ... Throughout the book numerous examples of Lagrangian and Hamiltonian systems are included ... . It is very clearly written and it will be especially useful both for beginning researchers and for graduate students in applied mathematics, physics, or engineering." ( M. Eugenia Rosado Mari a, Mathematical Reviews, May, 2018)
"The starting point of this impressive textbook is the important fact that there are remarkable situations where the variables that describe a dynamical system do not lie in a vector space (i.e., a simple at algebraic structure) but rather lie in a geometrical setting allowing the differential calculus, namely a differential manifold. ... In conclusion, this book is extremely useful for each reader who wishes to develop a modern knowledge of analytical mechanics." (Mircea Crâsmareanu, zbMATH 1381.70005, 2018)

"This well-written and expansive book is ambitious in its scope in that it aims at sound and thorough pedagogy as far as its subject matter is concerned, and it also aims at preparing the reader for computational work ... . There are many good examples accompanying or even guiding the text, as well as extensive problem sets for the properly serious student. This book ... prove very valuable to its readership, be they mathematicians, engineers, or physicists." (Michael Berg, MAA Reviews, November, 2017)