Symplectic Elasticity
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"Symplectic Elasticity" by Weian Yao, Wanxie Zhong, Chee Wah Lim is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Solid mechanics problems have long been regarded as bottlenecks in the development of elasticity. In contrast to traditional solution methodologies, such as Timoshenko's theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Departing from the conventional Euclidean space with one kind of variable, the symplectic space with dual variables thus provides a fundamental breakthrough. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in some detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics.
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"Symplectic Elasticity" by Weian Yao, Wanxie Zhong, Chee Wah Lim is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Dynamics
Author: Weian Yao, Wanxie Zhong, Chee Wah Lim
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
Solid mechanics problems have long been regarded as bottlenecks in the development of elasticity. In contrast to traditional solution methodologies, such as Timoshenko's theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Departing from the conventional Euclidean space with one kind of variable, the symplectic space with dual variables thus provides a fundamental breakthrough. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in some detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics.
| Author | Weian Yao, Wanxie Zhong, Chee Wah Lim |
| Publisher | World Scientific |
| Published | 2009 |
| ISBN-13 | 9789812778703 |
| Binding | Hardcover |
| Pages | 315 |
| Language | English |
| Subjects | Technology & Engineering |
| Topic | Dynamics |
Format: Hardcover
Length: 315 pages
Language: English
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