Variational Calculus with Engineering Applications

Name: Variational Calculus with Engineering Applications
Brand: Wiley
Price: 96.99 EUR
Availability: OnlineOnly

Constantin Udriste Ionel Tevy(Autor*in)

Wiley (Verlag)

1. Auflage

Erschienen am 14. Oktober 2022

224 Seiten

E-Book

PDF mit Adobe-DRM

Systemvoraussetzungen

978-1-119-94437-9 (ISBN)

96,99 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Adobe-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
Variational Calculus with Engineering Applications
Contents
Preface
1 Extrema of Differentiable Functionals
1.1 Differentiable Functionals
1.2 Extrema of Differentiable Functionals
1.3 Second Variation
Sufficient Conditions for Extremum
1.4 Optimum with Constraints
the Principle of Reciprocity
1.4.1 Isoperimetric Problems
1.4.2 The Reciprocity Principle
1.4.3 Constrained Extrema: The Lagrange Problem
1.5 Maple Application Topics
2 Variational Principles
2.1 Problems with Natural Conditions at the Boundary
2.2 Sufficiency by the Legendre-Jacobi Test
2.3 Unitemporal Lagrangian Dynamics
2.3.1 Null Lagrangians
2.3.2 Invexity Test
2.4 Lavrentiev Phenomenon
2.5 Unitemporal Hamiltonian Dynamics
2.6 Particular Euler-Lagrange ODEs
2.7 Multitemporal Lagrangian Dynamics
2.7.1 The Case of Multiple Integral Functionals
2.7.2 Invexity Test
2.7.3 The Case of Path-Independent Curvilinear Integral Functionals
2.7.4 Invexity Test
2.8 Multitemporal Hamiltonian Dynamics
2.9 Particular Euler-Lagrange PDEs
2.10 Maple Application Topics
3 Optimal Models Based on Energies
3.1 Brachistochrone Problem
3.2 Ropes, Chains and Cables
3.3 Newton's Aerodynamic Problem
3.4 Pendulums
3.4.1 Plane Pendulum
3.4.2 Spherical Pendulum
3.4.3 Variable Length Pendulum
3.5 Soap Bubbles
3.6 Elastic Beam
3.7 The ODE of an Evolutionary Microstructure
3.8 The Evolution of a Multi-Particle System
3.8.1 Conservation of Linear Momentum
3.8.2 Conservation of Angular Momentum
3.8.3 Energy Conservation
3.9 String Vibration
3.10 Membrane Vibration
3.11 The Schrödinger Equation in Quantum Mechanics
3.11.1 Quantum Harmonic Oscillator
3.12 Maple Application Topics
4 Variational Integrators
4.1 Discrete Single-time Lagrangian Dynamics
4.2 Discrete Hamilton's Equations
4.3 Numeric Newton's Aerodynamic Problem
4.4 Discrete Multi-time Lagrangian Dynamics
4.5 Numerical Study of the Vibrating String Motion
4.5.1 Initial Conditions for Infinite String
4.5.2 Finite String, Fixed at the Ends
4.5.3 Monomial (Soliton) Solutions
4.5.4 More About Recurrence Relations
4.5.5 Solution by Maple via Eigenvalues
4.5.6 Solution by Maple via Matrix Techniques
4.6 Numerical Study of the Vibrating Membrane Motion
4.6.1 Monomial (Soliton) Solutions
4.6.2 Initial and Boundary Conditions
4.7 Linearization of Nonlinear ODEs and PDEs
4.8 Von Neumann Analysis of Linearized Discrete Tzitzeica PDE
4.8.1 Von Neumann Analysis of Dual Variational Integrator Equation
4.8.2 Von Neumann Analysis of Linearized Discrete Tzitzeica Equation
4.9 Maple Application Topics
5 Miscellaneous Topics
5.1 Magnetic Levitation
5.1.1 Electric Subsystem
5.1.2 Electromechanic Subsystem
5.1.3 State Nonlinear Model
5.1.4 The Linearized Model of States
5.2 The Problem of Sensors
5.2.1 Simplified Problem
5.2.2 Extending the Simplified Problem of Sensors
5.3 The Movement of a Particle in Non-stationary Gravito-vortex Field
5.4 Geometric Dynamics
5.4.1 Single-time Case
5.4.2 The Least Squares Lagrangian in Conditioning Problems
5.4.3 Multi-time Case
5.5 The Movement of Charged Particle in Electromagnetic Field
5.5.1 Unitemporal Geometric Dynamics Induced by Vector Potential
5.5.2 Unitemporal Geometric Dynamics Produced by Magnetic Induction
5.5.3 Unitemporal Geometric Dynamics Produced by Electric Field
5.5.4 Potentials Associated to Electromagnetic Forms
5.5.5 Potential Associated to Electric 1-form
5.5.6 Potential Associated to Magnetic 1-form
5.5.7 Potential Associated to Potential 1-form
5.6 Wind Theory and Geometric Dynamics
5.6.1 Pendular Geometric Dynamics and Pendular Wind
5.6.2 Lorenz Geometric Dynamics and Lorenz Wind
5.7 Maple Application Topics
6 Nonholonomic Constraints
6.1 Models With Holonomic and Nonholonomic Constraints
6.2 Rolling Cylinder as a Model with Holonomic Constraints
6.3 Rolling Disc (Unicycle) as a Model with Nonholonomic Constraint
6.3.1 Nonholonomic Geodesics
6.3.2 Geodesics in Sleigh Problem
6.3.3 Unicycle Dynamics
6.4 Nonholonomic Constraints to the Car as a Four-wheeled Robot
trailer
6.5 Nonholonomic Constraints to the
6.6 Famous Lagrangians
6.7 Significant Problems
6.8 Maple Application Topics
7 Problems: Free and Constrained Extremals
7.1 Simple Integral Functionals
7.2 Curvilinear Integral Functionals
7.3 Multiple Integral Functionals
7.4 Lagrange Multiplier Details
7.5 Simple Integral Functionals with ODE Constraints
7.6 Simple Integral Functionals with Nonholonomic Constraints
7.7 Simple Integral Functionals with Isoperimetric Constraints
7.8 Multiple Integral Functionals with PDE Constraints
7.9 Multiple Integral Functionals With Nonholonomic Constraints
7.10 Multiple Integral Functionals With Isoperimetric Constraints
7.11 Curvilinear Integral Functionals With PDE Constraints
7.12 Curvilinear Integral Functionals With Nonholonomic Constraints
7.13 Curvilinear Integral Functionals with Isoperimetric Constraints
7.14 Maple Application Topics
Bibliography
Index
EULA

Systemvoraussetzungen

Als PDF speichern Als Link merken