The Principle of Least Action in Geometry and Dynamics

The Principle of Least Action in Geometry and Dynamics PDF

Author: Karl Friedrich Siburg

Publisher: Springer Science & Business Media

Published: 2004-05-17

Total Pages: 148

ISBN-13: 9783540219446

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New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.

Principles of Brain Dynamics

Principles of Brain Dynamics PDF

Author: Mikhail I. Rabinovich

Publisher: MIT Press

Published: 2023-12-05

Total Pages: 371

ISBN-13: 0262549905

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Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a constant environment. The application of nonlinear dynamics to the study of brain activity began to flourish in the 1990s when combined with empirical observations from modern morphological and physiological observations. This book offers perspectives on brain dynamics that draw on the latest advances in research in the field. It includes contributions from both theoreticians and experimentalists, offering an eclectic treatment of fundamental issues. Topics addressed range from experimental and computational approaches to transient brain dynamics to the free-energy principle as a global brain theory. The book concludes with a short but rigorous guide to modern nonlinear dynamics and their application to neural dynamics.

Analytical Mechanics

Analytical Mechanics PDF

Author: J.L. Lagrange

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 634

ISBN-13: 9401589038

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The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.

Advanced Dynamics

Advanced Dynamics PDF

Author: Donald T. Greenwood

Publisher: Cambridge University Press

Published: 2006-11-02

Total Pages: 437

ISBN-13: 0521029937

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A broad and detailed description of dynamics for mechanical and aerospace engineering applications.

Principles of Dynamics

Principles of Dynamics PDF

Author: R. C. Hibbeler

Publisher: Prentice Hall

Published: 2005

Total Pages: 510

ISBN-13:

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For introductory dynamics courses found in mechanical engineering, civil engineering, aeronautical engineering, and engineering mechanics departments. This 400 page paperback text contains all the topics and examples of the bestselling hardback text, and free access to Hibbeler's Onekey course where instructors select and post assignments. All this comes with significant savings for students! Hibbeler's course contains over 3,000 Statics and Dynamics problems instructors can personalize and post for student assignments. OneKey lets instructors edit the values in a problem, guaranteeing a fresh problem for the students, and then use use MathCAD solutions worksheets to generate solutions for use in grading (and post for student review). Each problem also comes with optional student hints and an assignment guide. PHGradeAssist - Hibbeler's PHGradeassist course contains over 600 Statics and Dynamics problems an instructor can use to generate algorithmic homework. PHGA grades and tracks student answers and performance, and offers sample solutions as feedback. Students will also find a complete Activebook (cross referenced in hints) as well as a set of animations and simulations for use on-line. Professors will find complete support including Powerpoints, JPEGS, Active Learning Slides for CRS systems, Matlab/Mathcad support, and student Math Review Of course, the Hibbeler Principles book retains all it's core features that make it the most student friendly book on the market -- the most examples, 3D photrealistic artwork, Procedure for Analysis problem solving boxes, triple accuracy checking, photgraphs that teach, and a carefully-crafted, student centered design.

Classical Dynamics

Classical Dynamics PDF

Author: Donald T. Greenwood

Publisher: Courier Corporation

Published: 2012-05-04

Total Pages: 368

ISBN-13: 0486138798

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Graduate-level text provides strong background in more abstract areas of dynamical theory. Hamilton's equations, d'Alembert's principle, Hamilton-Jacobi theory, other topics. Problems and references. 1977 edition.