Geometric Mechanics and Its Applications

Weipeng Hu; Chuan Xiao; Zichen Deng

doi:10.1007/978-981-19-7435-9

Geometric Mechanics and Its Applications

Weipeng Hu, Chuan Xiao, Zichen Deng

School of Aeronautics

Research output: Book/Report › Book › peer-review

4 Scopus citations

Abstract

To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

Original language	English
Publisher	Springer Nature
Number of pages	531
ISBN (Electronic)	9789811974359
ISBN (Print)	9789811974342
DOIs	https://doi.org/10.1007/978-981-19-7435-9
State	Published - 1 Jan 2023

Keywords

Astrodynamics
Conservation Law
Dissipation
Dynamic Symmetry Breaking
Dynamic System
Generalized Multi-symplectic Method
Geometric Mechanics
Hamiltonian
Impact Dynamics
Structure-preserving
Symmetry

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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Cite this

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AU - Xiao, Chuan

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N2 - To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

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Geometric Mechanics and Its Applications

Abstract

Keywords

UN SDGs

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