Nonlinear Problems of Engineering

ContributorsForewordPrefaceNew Methods in Nonlinear Mechanics I. Introduction II. The Comparative Approach III. Classical Approach IV. Discussion V. The New Approach of Invariant Imbedding VI. Discussion VII. Variational Processes VIII. Geodesics IX. Dynamic Programming and the Calculus of Variations X. Approximation in Policy Space XI. Discussion ReferencesProbability as a ScienceOn Random Solutions of Nonlinear Integral Equations Text ReferencesA Singular Case of Iteration of Analytic Functions: A Contribution to the Small-Divisor Problem I. The "Center Problem" in the Iteration of Analytic Functions II. Contexts Leading to Small-Divisor Series III. Generalities Regarding Iteration of Analytic Functions IV. Construction of Singular Iterations Zn+1 = f(Zn) V. Properties of Singular Iterations ReferencesNetworks of Inextensible Cords I. Introduction II. Pure Homogeneous Deformation III. Plane Strain of a Net-Displacement Boundary Conditions IV. Plane Strain of a Net-Force Boundary Conditions V. Further Developments BibliographyOn Integral Operators Generating Stream Functions of Compressible Fluids Introduction I. Partial Differential Equations Arising in the Theory of Compressible Fluids II. The Determination of the Stream Function of a Vortex in the Subsonic Region III. A Method for Generating Solutions of Equation (1.3.5) References BibliographySome Problems Concerning Linear Differential Equations Made Nonlinear by Unknown or Moving Boundaries A. Melting or Solidification B. Consolidation of an Earth Dam C. Seepage through a Porous Dam D. Lubrication in a Journal Bearing, with Oil Cavitation References General ReferencesNonlinear Problems of Combined Conductive-Radiative Heat Transfer Nomenclature Introduction The Single Plate-Type Fin Radiant Interaction Between Fin and Tube Surfaces Radiant Interaction Between Fin Surfaces Radiant Interaction Between Fin and Tube and Between Neighboring Fins Concluding Remarks ReferencesStatistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation I. A Particular Nonlinear Partial Differential Equation and Its Solution by Means of a Geometrical Construction II. Formulation of a Statistical Problem III. The Solution of the Auxiliary Differential Equation NotesMelting Decelerating Bodies Introduction Symbols Analysis Results Concluding Remarks ReferencesThermal Radiation Effects on Hypersonic Flow Fields I. Introduction II. Fundamentals of Radiant Energy Transfer III. Fundamental Equations of Radiation Gas Dynamics IV. Solutions for Radiation Transfer Equation V. New Parameters of Radiation Gas Dynamics VI. Wave Motions in Radiation Gas Dynamics VII. Shock Waves in Radiation Gas Dynamics VIII. Jet Mixing in Radiation Gas Dynamics IX. Plane Couette Flow in Radiation Magnetogas Dynamics ReferencesMathematical Theory of Compressible Fluids Introduction List of Symbols 1. Two-Dimensional Compressible Flow in the Physical Plane 2. Two-Dimensional Compressible Flow in the Hodograph Plane 3. Two-Dimensional Compressible Flow About a Closed Body in a Uniform Subsonic Flow 4. Two-Dimensional Flow through the Sonic Line ReferencesProblems in Nonlinear Nonmechanics Introduction Information and Communication Symbols and Symbolic Structure Handicaps and Communication Other Observations Concluding Remarks ReferencesNonlinear Problems in Ballistics Text ReferencesAlternating Direction Methods for Solving Partial Difference Equations 1. Introduction 2. The Difference Equation 3. The Linear System 4. The Peaceman-Rachford Method 5. The Cummutative Case 6. Laminar Flow Problem 7.