-
大小: 6.41MB文件类型: .pdf金币: 1下载: 0 次发布日期: 2023-11-01
- 语言: 其他
- 标签: Variational Applications
资源简介
1 Preliminaries 3
1.1 A Bit of History 4
1.2 Introduction 7
1.3 Motivation 8
1.3.1 Optics 8
1.3.2 Shape of a Liquid Drop 10
1.3.3 Optimization of a River-Crossing Trajectory 12
1.3.4 Summary 14
1.4 Extrema of Functions 14
1.5 Constrained Extrema and Lagrange Multipliers 17
1.6 Integration by Parts 20
1.7 Fundamental Lemma of the Calculus of
Variations 21
1.8 Adjoint and Self-Adjoint Differential Operators 22
Exercises 26
2 Calculus of Variations 28
2.1 Functionals of One Independent Variable 29
2.1.1 Functional Derivative 30
2.1.2 Derivation of Euler’s Equation 31
2.1.3 Variational Notation 33
2.1.4 Special Cases of Euler’s Equation 37
2.2 Natural Boundary Conditions 44
2.3 Variable End Points 53
2.4 Higher-Order Derivatives 56
2.5 Functionals of Two Independent Variables 56
2.5.1 Euler’s Equation 57
2.5.2 Minimal Surfaces 61
2.5.3 Dirichlet Problem 62
vii
viii Contents
2.6 Functionals of Two Dependent Variables 64
2.7 Constrained Functionals 66
2.7.1 Integral Constraints 66
2.7.2 Sturm-Liouville Problems 74
2.7.3 Algebraic and Differential Constraints 76
2.8 Summary of Euler Equations 80
Exercises 81
3 Rayleigh-Ritz, Galerkin, and Finite-Element Methods 90
3.1 Rayleigh-Ritz Method 91
3.1.1 Basic Procedure 91
3.1.2 Self-Adjoint Differential Operators 94
3.1.3 Estimating Eigenvalues of Differential Operators 96
3.2 Galerkin Method 100
3.3 Finite-Element Methods 103
3.3.1 Rayleigh-Ritz–Based Finite-Element Method 104
3.3.2 Finite-Element Methods in Multidimensions 109
Exercises 110
P A R T I I P H Y S I C A L A P P L I C A T I O N S 115
4 Hamilton’s Principle 117
4.1 Hamilton’s Principle for Discrete Systems 118
4.2 Hamilton’s Principle for Continuous Systems 128
4.3 Euler-Lagrange Equations 131
4.4 Invariance of the Euler-Lagrange Equations 136
4.5 Derivation of Hamilton’s Principle from the First Law of
Thermodynamics 137
4.6 Conservation of Mechanical Energy and the Hamiltonian 141
4.7 Noether’s Theorem – Connection Between
Conservation Laws and Symmetries in Hamil
代码片段和文件信息
相关资源
- Geometric Functional Analysis and Its Applicat
- Computational Geometry - Algorithms and Applic
- Fast Data Architectures For Streaming Applicat
- Jaya. An advanced Optimization Algorithm and i
- An Introduction to Stochastic Processes with A
- Designing Data-Intensive Applications_高清PD
- Data Clustering Theory Algorithms and Applicat
- Introduction-to-Digital-Filters-with-Audio-App
- Debugging Applications windows程序调试中文
- 线性代数及其应用Linear Algebra and Its
-
ob
ject-Oriented Analysis and Design with Ap - Linear Algebra and Its Applications 5th David
- Internal Flow - Concepts and Applications
- Numerical Liner Algebra with Applications
-
Disturbance Observer-ba
sed Control_ Methods - GNSS Applications and Methods.pdf
- Phase-Locked Loops Design Simulation and Appli
- Manifolds Tensor Analysis and Applications
- Electromagnetic Compatibility Principles and A
- Gaussian Markov Random Fields:Theory and App
- image recognition and classification_algorithm
- Manifold learning theory and applications2011清
- -AC Electric Motors Control_ Advanced Design T
- Image processing and analysis variational PDE
- Fast Fourier Transform and Its Applications
- GNSSApplicationsandMethods.pdf
- zw_DiscreteMathematicsandItsApplications7thKen
- Computational+Geometry+-+Algorithms+and+Applic
- Testing Vue.js Applications
- 深度学习金融应用综述Deep Learning fo
评论
共有 条评论