The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Editor: Courier Corporation
ISBN: 0486134709
Size: 14,94 MB
Format: PDF, ePub
Read: 412
Download

Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

The Variational Principles Of Mechanics

Author: Lánczos Kornél
Editor:
ISBN:
Size: 19,60 MB
Format: PDF
Read: 435
Download


The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Editor:
ISBN:
Size: 12,87 MB
Format: PDF, ePub
Read: 515
Download


The Variational Principles Of Mechanics

Author: Cornelius Lanczos (Physicist, Mathematician, Hungary, Germany, United States)
Editor:
ISBN:
Size: 13,62 MB
Format: PDF, ePub, Docs
Read: 410
Download


Variational Principles In Dynamics And Quantum Theory

Author: Wolfgang Yourgrau
Editor: Courier Corporation
ISBN: 9780486637730
Size: 19,14 MB
Format: PDF, ePub, Docs
Read: 296
Download

Historical, theoretical survey with many insights, much hard-to-find material. Covers Hamilton's principle, Hamilton-Jacobi equation, relationship to quantum theory and wave mechanics, and more.

Variational Principles Of Continuum Mechanics

Author: Victor Berdichevsky
Editor: Springer Science & Business Media
ISBN: 354088467X
Size: 18,26 MB
Format: PDF, ePub
Read: 253
Download

Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

Classical Mechanics With Calculus Of Variations And Optimal Control

Author: Mark Levi
Editor: American Mathematical Soc.
ISBN: 0821891383
Size: 14,16 MB
Format: PDF, Kindle
Read: 679
Download

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.

Variational Principles In Classical Mechanics

Author: Douglas Cline
Editor:
ISBN: 9780998837277
Size: 12,63 MB
Format: PDF, Docs
Read: 132
Download

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.

The Variational Principles Of Mechanics

Author: Cornelius Lanczos (Physicist, Mathematician, Hungary, Germany, United States)
Editor:
ISBN:
Size: 20,68 MB
Format: PDF, ePub, Mobi
Read: 497
Download


The Variational Principles Of Dynamics

Author: Boris A Kupershmidt
Editor: World Scientific Publishing Company
ISBN: 9813103655
Size: 16,56 MB
Format: PDF, Kindle
Read: 259
Download

Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader. Request Inspection Copy