Overview
- Offers a state-of-the-art overview of rigid body dynamics, covering the fundamentals as well as advances in research
- Collects all known integrable cases in one convenient volume, which were previously scattered throughout the literature
- Presents for the first time in English all twelve known solutions of the equations of motion in the classical problem
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 45)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (14 chapters)
-
Front Matter
-
The Elementary Part
-
Front Matter
-
-
The Advanced Part
-
Front Matter
-
-
Back Matter
Keywords
- Rigid body dynamics
- Lagrangian mechanics
- Equations of motion
- Integrable systems
- Motion of a body in a liquid
- Rigid body fixed point
- Rigid body integrable cases
- Rigid body integrability
- Rigid body motion
- Rigid body transformation
- Lagrangian approach
- Euler-Lagrange equations
- Euler-Poincare equations
- Legendre transformations
- Rotation matrix
- Hamiltonian form
About this book
This monograph provides a complete and up-to-date examination of rigid body dynamics using a Lagrangian approach. All known integrable cases, which were previously scattered throughout the literature, are collected here for convenient reference. Also contained are particular solutions to diverse problems treated within rigid body dynamics.
The first seven chapters introduce the elementary dynamics of the rigid body and its main problems. A full historical account of the discovery and development of each of the integrable cases is included as well. Instructors will find this portion of the book well-suited for an undergraduate course, having been formulated by the author in the classroom over many years.
The second part includes more advanced topics and some of the author’s original research, highlighting several unique methods he developed that have led to significant results. Some of the specific topics covered include the twelve known solutions of the equations of motion in the classical problem, which has not previously appeared in English before; a collection of completely new integrable cases; and the motion of a rigid body around a fixed point under the action of an asymmetric combination of potential and gyroscopic forces.Rigid Body Dynamics will appeal to researchers in the area as well as those studying dynamical and integrable systems theory.
Reviews
Authors and Affiliations
Bibliographic Information
Book Title: Rigid Body Dynamics
Book Subtitle: A Lagrangian Approach
Authors: Hamad M. Yehia
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-030-96336-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-96335-4Published: 28 June 2022
Softcover ISBN: 978-3-030-96338-5Published: 29 June 2023
eBook ISBN: 978-3-030-96336-1Published: 27 June 2022
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: XXV, 460
Number of Illustrations: 25 b/w illustrations, 52 illustrations in colour
Topics: Applications of Mathematics, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Classical Mechanics, Solid Mechanics, Mathematical Physics