Note: 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 -- 1.10 Some Elementary Examples Involving Integral Variational Principles -- 1.11 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 -- 3.2 Simultaneous and Nonsimultaneous Variations. Infinitesimal Transformations -- 3.3 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 -- 3.10 Inclusion of Generalized Nonconservative Forces in the Search for Conservation Laws. D'Alembert's Principle. , 3.11 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 -- 3.15 Conservation Laws of Conservative and Nonconservative Dynamical Systems Obtained by Means of the Differential Variational Principles of Gauss and Jourdain -- 3.16 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 -- Chapter 4. A Study of the Motion of Conservative and Nonconservative Dynamical Systems by Means of Field Theory -- 4.1 Introduction -- 4.2 Hamilton's Canonical Equations of Motion -- 4.3 Integration of Hamilton's Canonical Equations by Means of the Hamilton-Jacobi Method -- 4.4 Separation of Variables in the Hamilton-Jacobi Equation -- 4.5 Application of the Hamilton-Jacobi Method to Linear Nonconservative Oscillatory Systems -- 4.6 A Field Method for Nonconservative Dynamical Systems -- 4.7 The Complete Solutions of the Basic Field Equation and Their Properties -- 4.8 The Single Solutions of the Basic Field Equation -- 4.9 Illustrative Examples -- 4.10 Applications of the Complete Solutions of the Basic Field Equation to Two-Point Boundary-value Problems. , 4.11 The Potential Method of Arzhanik'h for Nonconservative Dynamical Systems -- 4.12 Applications of the Field Method to Nonlinear Vibration Problems -- 4.13 A Linear Oscillator with Slowly Varying Frequency -- 4.14 References -- Chapter 5. Variational Principles with Vanishing Parameters and Their Applications -- 5.1 Introduction -- 5.2 A Short Review of Some Variational Formulations Frequently Used in Nonconservative Field Theory -- 5.3 The Variational Principle with Vanishing Parameter -- 5.4 Application of the Direct Method of Partial Integration to the Solution of Linear and Nonlinear Boundary-Value Problems -- 5.5 An Example: A Semi-Infinite Body with a Constant Heat Flux Input -- 5.6 A Semi-Infinite Body with an Arbitrary Heat Flux Input -- 5.7 The Temperature Distribution in a Body Whose End is Kept at Constant Temperature, Temperature-Dependent Thermophysical Coefficients -- 5.8 The Moment-Lagrangian Method -- 5.9 The Temperature Distribution in a Finite Rod with a Nonzero Initial Temperature Distribution -- 5.10 The Temperature Distribution in a Noninsulated Solid -- 5.11 Applications to Laminar Boundary Layer Theory -- 5.12 Applications to Two-Dimensional Boundary Layer Flow of Incompressible, Non-Newtonian Power-Law Fluids -- 5.13 A Variational Solution of the Rayleigh Problem for a Non-Newtonian Power-Law Conducting Fluid -- 5.14 References -- Chapter 6. Variational Principles with Uncommutative Rules and Their Applications to Nonconservative Phenomena -- 6.1 Introduction -- 6.2 The Variational Principle with Uncommutative Rules -- 6.3 The Connection (Relation) between the Variational Principle with Uncommutative Rules and the Central Lagrangian Equation -- 6.4 The Bogoliubov-Krylov-Mitropolsky Method in Nonlinear Vibration Analysis as a Variational Problem -- 6.5 Applications to Heat Conduction in Solids -- 6.6 References. , Chapter 7. Applications of Gauss's Principle of Least Constraint to Nonconservative Phenomena -- 7.1 Introduction -- 7.2 Methods of Approximation Based on the Gauss Principle of Least Constraint -- 7.3 Applications to Ordinary Differential Equations -- 7.4 Applications to Transient, Two-Dimensional, Nonlinear Heat Conduction through Prism-Like Infinite Bodies with a Given Cross Section -- 7.5 Melting or Freezing of a Semi-Infinite Solid -- 7.6 A Semi-Infinite Solid with an Arbitrary Heat Flux Input: Gauss's Approach -- 7.7 A Nonconservative Convective Problem -- 7.8 References -- Author Index -- Index -- Mathematics in Science and Engineering.