Variational calculus with engineering applications / / Constantin Udriște and Ionel Tevy

• Record Nr.: UNINA9910830944903321
• Autore: Udriște Constantin
• Pubbl/distr/stampa: Hoboken, New Jersey ; ; Chichester, West Sussex, England : , : Wiley, , [2023]; ©2023
• ISBN: 1-119-94442-2; 1-119-94437-6
• Descrizione fisica: 1 online resource (224 pages)
• Disciplina: 515.64
• Soggetti: Calculus of variations; Engineering mathematics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references (pages 214-219) and index.
• Nota di contenuto: 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.