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A Primer on the Kinematics of Discrete Elastic Rods

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  • Adopts a comprehensive, yet short, introduction to a new and promising numerical formulation

  • Reinforces concepts with worked examples expressed in a consistent notation

  • Presented in sufficient detail for the reader versed in mechanics to start using discrete elastic rod formulation in problems

  • Features an introduction to widely cited works published in the past decade

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

Part of the book sub series: SpringerBriefs in Thermal Engineering and Applied Science (BRIEFSTHERMAL)

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USD 54.99
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  • ISBN: 978-3-319-76965-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book
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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introduction

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 1-9
  3. Kirchhoff’s Theory of an Elastic Rod

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 11-23
  4. The Discretized Curve: Vertices, Edges, and Curvature

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 25-32
  5. Bishop Frames and Reference Frames Along the Discretized Curve

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 33-46
  6. Material Frames and Measures of Twists

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 47-57
  7. Variations, Gradients, and Hessians

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 59-73
  8. Spherical Excess and Reference Twist

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 75-92
  9. Equations of Motion and Energetic Considerations

    • M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly
    Pages 93-112
  10. Back Matter

    Pages 113-118

About this book

This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou, et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou, et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.

Keywords

  • Rod theory
  • Miklós Bergou
  • numerical methods
  • discrete elastic rods
  • mechanics of rods

Authors and Affiliations

  • Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, USA

    M. Khalid Jawed

  • Department of Mechanical Engineering, University of California, Berkeley, Berkeley, USA

    Alyssa Novelia, Oliver M. O'Reilly

About the authors

Dr. ​M. Khalid Jawed is an Assistant Professor in the Department of Mechanical and Aerospace Engineering at the University of California, Los Angeles. 

Alyssa Novelia is a graduate student in the Department of Mechanical Engineering at the University of California, Berkeley. 

Dr. Oliver M. O’Reilly is a Professor in the Department of Mechanical Engineering at the University of California, Berkeley.

Bibliographic Information

  • Book Title: A Primer on the Kinematics of Discrete Elastic Rods

  • Authors: M. Khalid Jawed, Alyssa Novelia, Oliver M. O'Reilly

  • Series Title: SpringerBriefs in Applied Sciences and Technology

  • DOI: https://doi.org/10.1007/978-3-319-76965-3

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-76964-6

  • eBook ISBN: 978-3-319-76965-3

  • Series ISSN: 2191-530X

  • Series E-ISSN: 2191-5318

  • Edition Number: 1

  • Number of Pages: XIII, 118

  • Number of Illustrations: 44 illustrations in colour

  • Topics: Engineering Mechanics, Engineering Mathematics, Classical Mechanics

Buying options

eBook
USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-76965-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 69.99
Price excludes VAT (USA)