UID:
almahu_9947367293502882
Umfang:
1 online resource (383 p.)
ISBN:
1-282-03473-1
,
9786612034732
,
0-08-092642-8
Serie:
Mathematics in science and engineering ; v. 182
Inhalt:
This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include
Anmerkung:
Description based upon print version of record.
,
Front Cover; Variational Methods in Nonconservative Phenomena; Copyright Page; Contents; Preface; Chapter 1. A Brief Account of the Variational Principles of Classical Holonomic Dynamics; 1.1 Introduction; 1.2 Constraints and the Forces of Constraint; 1.3 Actual and Virtual Displacements; 1.4 D' Alembert's Principle; 1.5 The Lagrangian Equations with Multipliers; 1.6 Generalized Coordinates. Lagrangian Equations; 1.7 A Brief Analysis of the Lagrangian Equations; 1.8 Hamilton's Principle; 1.9 Variational Principles Describing the Paths of Conservative Dynamical Systems
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1.10 Some Elementary Examples Involving Integral Variational Principles1.11 References; Chapter 2. Variational Principles and Lagrangians; 2.1 Introduction; 2.2 Lagrangians for Systems with One Degree of Freedom; 2.3 Quadratic Lagrangians for Systems with One Degree of Freedom; 2.4 Some Other Lagrangians; 2.5 The Inverse Problem of the Calculus of Variations; 2.6 Partial Differential Equations; 2.7 Lagrangians with Vanishing Parameters; 2.8 Other Variational Principles; 2.9 References; Chapter 3. Conservation Laws; 3.1 Introduction
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3.2 Simultaneous and Nonsimultaneous Variations. Infinitesimal Transformations3.3 The Condition of Invariance of Hamilton's Action Integral. Absolute and Gauge Invariance; 3.4 The Proof of Noether's Theorem. Conservation Laws; 3.5 The Inertial Motion of a Dynamical System. Killing's Equations; 3.6 The Generalized Killing Equations; 3.7 Some Classical Conservation Laws of Dynamical Systems Completely Described by a Lagrangian Function; 3.8 Examples of Conservation Laws of Dynamical Systems; 3.9 Some Conservation Laws for the Kepler Problem
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3.10 Inclusion of Generalized Nonconservative Forces in the Search for Conservation Laws. D'Alembert's Principle3.11 Inclusion of Nonsimultaneous Variations into the Central Lagrangian Equation; 3.12 The Conditions for Existence of a Conserved Quantity. Conservation Laws of Nonconservative Dynamical Systems; 3.13 The Generalized Killing Equations for Nonconservative Dynamical Systems; 3.14 Conservation Laws of Nonconservative Systems Obtained by Means of Variational Principles with Noncommutative Variational Rules
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3.15 Conservation Laws of Conservative and Nonconservative Dynamical Systems Obtained by Means of the Differential Variational Principles of Gauss and Jourdain3.16 Jourdainian and Gaussian Nonsimultaneous Variations; 3.17 The Invariance Condition of the Gauss Constraint; 3.18 An Equivalent Transformation of Jourdain's Principle; 3.19 The Conservation Laws of Schul'gin and Painlevé; 3.20 Energy-Like Conservation Laws of Linear Nonconservative Dynamical Systems; 3.21 Energy-Like Conservation Laws of Linear Dissipative Dynamical Systems; 3.22 A Special Class of Conservation Laws; 3.23 References
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Chapter 4. A Study of the Motion of Conservative and Nonconservative Dynamical Systems by Means of Field Theory
,
English
Weitere Ausg.:
ISBN 0-12-728450-8
Sprache:
Englisch
