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Calculus of variations : mechanics, control and other applications

Author: C R MacCluer
Publisher: Mineola, N.Y. : Dover Publications, 2012.
Series: Dover books on mathematics.
Edition/Format:   eBook : Document : English : Dover edView all editions and formats
Summary:
First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
MacCluer, C.R.
Calculus of variations.
Mineola, N.Y. : Dover Publications, 2012
(DLC) 2012013550
(OCoLC)784125866
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: C R MacCluer
ISBN: 9780486278308 0486278301
OCLC Number: 841494439
Notes: Originally published: Upper Saddle River, N.J. : Prentice Hall, ©2005.
Description: 1 online resource (x, 254 pages).
Contents: Cover Page; Title Page; Copyright Page; Dedication; Contents; 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 ConstraintsExercises; 6 Extremal Surfaces; 6.1 A Soap Film (CVP 15); 6.2 Stable Flows (CVP 17); 6.3 Schrödinger'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 ServoExercises; 9 Weak Sufficiency; 9.1 Weak versus Strong Extrema; 9.2 First and Second Variations; 9.3 In Application; 9.4 The Integrand p[eta]'2 + q[eta]2; 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 TheoremAppendix C. The Divergence Theorem; Appendix D.A MATLAB Cookbook; References; Index; Back Cover.
Series Title: Dover books on mathematics.
Responsibility: Charles R. MacCluer.
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Abstract:

First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.

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