Classical Mechanics With Calculus Of Variations And Optimal Control

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Classical Mechanics with Calculus of Variations and Optimal Control

Author : Mark Levi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891383
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classical Mechanics with Calculus of Variations and Optimal Control by : Mark Levi

Download or read book Classical Mechanics with Calculus of Variations and Optimal Control written by Mark Levi and published by American Mathematical Soc.. This book was released on 2014-03-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Calculus of Variations and Optimal Control Theory

Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Calculus of Variations

Author : Charles R. MacCluer
Publisher : Courier Corporation
ISBN 13 : 0486278301
Total Pages : 274 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Calculus of Variations by : Charles R. MacCluer

Download or read book Calculus of Variations written by Charles R. MacCluer and published by Courier Corporation. This book was released on 2013-05-20 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Calculus of Variations and Optimal Control

Author : George Leitmann
Publisher : Springer Science & Business Media
ISBN 13 : 148990333X
Total Pages : 313 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis The Calculus of Variations and Optimal Control by : George Leitmann

Download or read book The Calculus of Variations and Optimal Control written by George Leitmann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Functional Analysis, Calculus of Variations and Optimal Control

Author : Francis Clarke
Publisher : Springer Science & Business Media
ISBN 13 : 1447148207
Total Pages : 589 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Functional Analysis, Calculus of Variations and Optimal Control by : Francis Clarke

Download or read book Functional Analysis, Calculus of Variations and Optimal Control written by Francis Clarke and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

The Calculus of Variations and Functional Analysis

Author : L. P. Lebedev
Publisher : World Scientific
ISBN 13 : 9812794999
Total Pages : 435 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis The Calculus of Variations and Functional Analysis by : L. P. Lebedev

Download or read book The Calculus of Variations and Functional Analysis written by L. P. Lebedev and published by World Scientific. This book was released on 2003 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is aimed at those who are concerned about Chinese medicine - how it works, what its current state is and, most important, how to make full use of it. The audience therefore includes clinicians who want to serve their patients better and patients who are eager to supplement their own conventional treatment. The authors of the book belong to three different fields, modern medicine, Chinese medicine and pharmacology. They provide information from their areas of expertise and concern, attempting to make it comprehensive for users. The approach is macroscopic and philosophical; readers convinced of the philosophy are to seek specific assistance.

Optimal Control and the Calculus of Variations

Author : Enid R. Pinch
Publisher : Oxford University Press
ISBN 13 : 0198514891
Total Pages : 245 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Optimal Control and the Calculus of Variations by : Enid R. Pinch

Download or read book Optimal Control and the Calculus of Variations written by Enid R. Pinch and published by Oxford University Press. This book was released on 1995 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. Theintorduction to optimal control begins by considering the problem of minimizing a function of many variables, before moving on to the main subject: the optimal control of systems governed by ordinary differential equations.

Variational Calculus with Elementary Convexity

Author : J.L. Troutman
Publisher : Springer Science & Business Media
ISBN 13 : 1468401580
Total Pages : 373 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Variational Calculus with Elementary Convexity by : J.L. Troutman

Download or read book Variational Calculus with Elementary Convexity written by J.L. Troutman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.

Variational Calculus and Optimal Control

Author : John L. Troutman
Publisher : Springer Science & Business Media
ISBN 13 : 1461207371
Total Pages : 471 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Variational Calculus and Optimal Control by : John L. Troutman

Download or read book Variational Calculus and Optimal Control written by John L. Troutman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.

Dynamic Optimization, Second Edition

Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien

Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

The Calculus of Variations

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
ISBN 13 : 0387216979
Total Pages : 295 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Calculus of Variations by : Bruce van Brunt

Download or read book The Calculus of Variations written by Bruce van Brunt and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

Introduction to the Calculus of Variations

Author : Hans Sagan
Publisher : Courier Corporation
ISBN 13 : 048613802X
Total Pages : 484 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to the Calculus of Variations by : Hans Sagan

Download or read book Introduction to the Calculus of Variations written by Hans Sagan and published by Courier Corporation. This book was released on 2012-04-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.

Introduction To The Fractional Calculus Of Variations

Author : Delfim F M Torres
Publisher : World Scientific Publishing Company
ISBN 13 : 184816968X
Total Pages : 292 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Introduction To The Fractional Calculus Of Variations by : Delfim F M Torres

Download or read book Introduction To The Fractional Calculus Of Variations written by Delfim F M Torres and published by World Scientific Publishing Company. This book was released on 2012-09-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a

The Mathematical Mechanic

Author : Mark Levi
Publisher : Princeton University Press
ISBN 13 : 1400830478
Total Pages : 197 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Mathematical Mechanic by : Mark Levi

Download or read book The Mathematical Mechanic written by Mark Levi and published by Princeton University Press. This book was released on 2009-07-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

Why Cats Land on Their Feet

Author : Mark Levi
Publisher : Princeton University Press
ISBN 13 : 1400841720
Total Pages : 205 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Why Cats Land on Their Feet by : Mark Levi

Download or read book Why Cats Land on Their Feet written by Mark Levi and published by Princeton University Press. This book was released on 2012-05-27 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to use physical reasoning to solve surprising paradoxes Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics. Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats. Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.

The Inverse Problem of the Calculus of Variations

Author : Dmitry V. Zenkov
Publisher : Springer
ISBN 13 : 9462391092
Total Pages : 296 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis The Inverse Problem of the Calculus of Variations by : Dmitry V. Zenkov

Download or read book The Inverse Problem of the Calculus of Variations written by Dmitry V. Zenkov and published by Springer. This book was released on 2015-10-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).

Optimal Control

Author : Arturo Locatelli
Publisher : Springer Science & Business Media
ISBN 13 : 9783764364083
Total Pages : 318 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Optimal Control by : Arturo Locatelli

Download or read book Optimal Control written by Arturo Locatelli and published by Springer Science & Business Media. This book was released on 2001-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control