Calculus of Variations: Mechanics, Control and Other Applications - Brossura

MacCluer, Charles R.

Brossura

ISBN 10: 0486498379 ISBN 13: 9780486498379

Casa editrice: Dover Pubns, 2012

Riassunto

The first truly up-to-date treatment of the calculus of variations, this text is also the first to offer a simple introduction to such key concepts as optimal control and linear-quadratic control design. Suitable for junior/senior–level students of math, science, and engineering, this volume also serves as a useful reference for engineers, chemists, and forest/environmental managers. Its broad perspective features numerous exercises, hints, outlines, and comments, plus several appendixes, including a practical discussion of MATLAB.
Students will appreciate the text's reader-friendly style, which features gradual advancements in difficulty and starts by developing technique rather than focusing on technical details. The examples and exercises offer many citations of engineering-based applications, and the exercises range from elementary to graduate-level projects, including longer projects and those related to classic papers.

Su questo libro

Recensione

The first truly up-to-date treatment of the calculus of variations, this text is also the first to offer a simple introduction to such key concepts as optimal control and linear-quadratic control design. Its broad perspective features numerous exercises, hints, outlines, and comments, plus several appendixes, including a practical discussion of MATLAB. Reprint of the Pearson Prentice Hall, Upper Saddle River, New Jersey, 2005 edition.

Contenuti

Preface Acknowledgments 1. Preliminaries 1.1 Directional Derivatives and Gradients 1.2 Calculus Rules 1.3 Contour Surfaces and Sublevel Sets 1.4 Lagrange Multipliers 1.5 Convexity Exercises 2. Optimization 2.1 Mathematical Programming 2.2 Linear Programming 2.3 Statistical Problems 2.4 Variational Problems Exercises 3. Formulating Variational Problems 3.1 Shortest Distance between Two Points (CVP 1) 3.2 Graph with Least Surface of Revolution (CVP 2) 3.3 The Catenary (CVP 3) 3.4 The Brachistochrone (CVP 4) 3.5 Cruise-Climb (CVP 5) 3.6 Shapes of Minimum Resistance (CVP 6) 3.7 Hamilton's Principle 3.8 Isoperimetric Problems Exercises 4. The Euler-Lagrange Equation 4.1 One Degree of Freedom 4.2 Two Special Cases: No y, No x 4.3 Multiple Degrees of Freedom 4.4 The Hamiltonian 4.5 A Closer Look Exercises 5. Constrained Problems 5.1 Dido's Problem 5.2 Statement of the Problem 5.3 The Inverse Function Theorem 5.4 The Euler-Lagrange Equation for Constrained Problems 5.5 Example Applications 5.6 Multiple Degrees of Freedom 5.7 Nonintegral Constraints 5.8 Hamilton's Principle with Constraints Exercises 6. Extremal Surfaces 6.1 A Soap Film (CVP 15) 6.2 Stable Flows (CVP 17) 6.3 Schrodinger's Equation (CVP 18) 6.4 Eigenvalue Problems 6.5 Rayleigh-Ritz Numerics Exercises 7. Optimal Control 7.1 A Rolling Cart (OCP 1) 7.2 General Formulation 7.3 Reinvestments (OCP 2) 7.4 Average Voltage (OCP 3) 7.5 A Time-Optimal Problem (OCP 4) 7.6 The Bang-Bang Principle 7.7 The Maximum Principle 7.8 Example Applications Exercises 8. The LQ Problem 8.1 Problem Statement 8.2 State Feedback 8.3 Stability 8.4 The LQR Problem 8.5 A Tracking Servo Exercises 9. Weak Sufficiency 9.1 Weak versus Strong Extrema 9.2 First and Second Variations 9.3 In Application 9.4 The Integrand 9.5 Weak Local Sufficiency Exercises 10. Strong Sufficiency 10.1 The Goal 10.2 Flows 10.3 Flows of the Euler-Lagrange Equation 10.4 The E-Function and Strong Sufficiency 10.5 The Existence of Flows Exercises 11. Corner Points 11.1 Corners and Extremals 11.2 First Erdmann Corner Condition 11.3 The Figurative 11.4 Second Erdmann Corner Condition Exercises Appendix A. The Inverse Function Theorem Appendix B. Picard's Theorem Appendix C. The Divergence Theorem Appendix D. A MATLAB Cookbook References Index

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 0486498379
• ISBN 13: 9780486498379
• Rilegatura: Copertina flessibile
• Numero di pagine: 254
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia