A Primer on the Kinematics of Discrete Elastic Rods

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.

List of contents

Discrete Elastic Rods.- Kirchhoff's Theory of an Elastic Rod.- Variations, Gradients, and Hessians.- Rotation of the Cross Section of the Rod, Spherical Excess, and Holonomy.- Kinetic Energy, Potential Energy, and Internal Forces.

About the author

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.

Summary

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.

Product details

• Authors: M Khali Jawed, M Khalid Jawed, M. Khalid Jawed, Alyss Novelia, Alyssa Novelia, Oliver M O'Reilly, Oliver M. O'Reilly
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319769646
• ISBN: 978-3-31-976964-6
• No. of pages: 118
• Dimensions: 156 mm x 235 mm x 8 mm
• Weight: 224 g
• Illustrations: XIII, 118 p. 44 illus. in color.
• Series: SpringerBriefs in Applied Sciences and Technology; SpringerBriefs in Thermal Engineering and Applied; SpringerBriefs in Applied Sciences and Technology; SpringerBriefs in Thermal Engineering and Applied Science; SpringerBriefs in Thermal Engineering and Applied
• Subjects: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering; C, Klassische Mechanik, Mathematik für Ingenieure, engineering, Civil Engineering, Classical mechanics, Theoretical and Applied Mechanics, Mechanics, Mechanics, Applied, Engineering mathematics, Maths for engineers