# Calculus of Variations: Mechanics, Control and Other Applications

## MacCluer, Charles R.

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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.

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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

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## 1.Calculus of Variations

Editore: Dover Pubns (2012)
ISBN 10: 0486498379 ISBN 13: 9780486498379
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Descrizione libro Dover Pubns, 2012. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486498379

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Descrizione libro Dover Publications Inc., 2012. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486498379

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## 4.Calculus of Variations: Mechanics, Control, and Other Applications (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2012. Paperback. Condizione libro: New. Reprint. 213 x 135 mm. Language: English . Brand New Book. An up-to-date treatment of the calculus of variations, this text also offers 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. Codice libro della libreria AAC9780486498379

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## 5.Calculus of Variations: Mechanics, Control, and Other Applications (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2012. Paperback. Condizione libro: New. Reprint. 213 x 135 mm. Language: English . Brand New Book. An up-to-date treatment of the calculus of variations, this text also offers 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. Codice libro della libreria AAC9780486498379

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Descrizione libro Paperback. Condizione libro: New. 135mm x 20mm x 213mm. Paperback. 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 .Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 254 pages. 0.272. Codice libro della libreria 9780486498379

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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 272 pages. Dimensions: 8.4in. x 5.3in. x 0.9in.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 juniorseniorlevel students of math, science, and engineering, this volume also serves as a useful reference for engineers, chemists, and forestenvironmental managers. Its broad perspective features numerous exercises, hints, outlines, and comments, plus several appendixes, including a practical discussion of MATLAB. Students will appreciate the texts 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486498379

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Descrizione libro Dover Publications Inc. Paperback. Condizione libro: new. BRAND NEW, Calculus of Variations: Mechanics, Control, and Other Applications, Charles R. MacCluer. Codice libro della libreria B9780486498379

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