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Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

A Geometric Approach to Modeling and Analysis

  • Taeyoung Lee
  • Melvin Leok
  • N. Harris McClamroch

Part of the Interaction of Mechanics and Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 1-51
  3. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 53-88
  4. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 89-129
  5. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 131-206
  6. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 207-271
  7. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 273-311
  8. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 313-346
  9. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 347-398
  10. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 399-484
  11. Taeyoung Lee, Melvin Leok, N. Harris McClamroch
    Pages 485-520
  12. Back Matter
    Pages 521-539

About this book

Introduction

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities.

The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems.

This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Keywords

Geometric Mechanics Lagrangian Systems Hamiltonian Systems Manifold Lie Groups Dynamics Mechanics Multibody Systems

Authors and affiliations

  1. 1.The George Washington UniversityWashington, District of ColumbiaUSA
  2. 2.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  3. 3.Department of Aerospace EngineeringThe University of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56953-6
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-56951-2
  • Online ISBN 978-3-319-56953-6
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • Buy this book on publisher's site