AN ELEMENTARY TREATISE ON KINEMATICS AND KINETICS

By L. RALIK

CONTENTS - I FUNDAMENTALS PART I FUNDAMENTALS VARIATIONAL PRINCIPLES PREHISTORY MOPERTUIS VARIATIONAL PRINCIPLE EULER’S CALCULUS OF VARIATIONS LAGRANGE VARIATIONAL PRINCIPLE JACOBI VARIATIONAL PRINCIPLE HAMILTON VARIATIONAL PRINCIPLE HAMILTONIAN EQUATIONS PHYSICAL MEANING OF THE LEAST ACTION PRINCIPLE THERMODYNAMICS THERMODYNAMIC DESCRIPTION TEMPERATURE ENTROPY ENTROPY AND PROBABILITY GIBBS PRINCIPLES NONEQUILIBRIUM PROCESSES SECONDARY THERMODYNAMICS AND HIGHER ORDER THERMODYNAMICS CONTINUUM MECHANICS CONTINUUM KINEMATICS BASIC LAWS OF CONTINUUM MECHANICS CLASSICAL CONTINUUM MODELS THERMODYNAMIC FORMALISM PRINCIPLE OF LEAST ACTION IN CONTINUUM MECHANICS VARIATION OF INTEGRAL FUNCTIONALS VARIATIONS OF KINEMATIC PARAMETERS PRINCIPLE OF LEAST ACTION VARIATIONAL EQUATIONS MODELS WITH HIGH DERIVATIVES TENSOR VARIATIONS DIRECT METHODS OF CALCULUS OF VARIATIONS INTRODUCTORY REMARKS QUADRATIC FUNCTIONALS EXISTENCE OF THE MINIMIZING ELEMENT UNIQUENESS OF THE MINIMIZING ELEMENT UPPER AND LOWER ESTIMATES DUAL VARIATIONAL PRINCIPLES LEGENDRE AND YOUNG-FENCHEL TRANSFORMATIONS EXAMPLES OF DUAL VARIATIONAL PRINCIPLES HASHIN-STRIKMAN VARIATIONAL PRINCIPLE VARIATIONAL PROBLEMS WITH CONSTRAINTS VARIATIONAL-ASYMPTOTIC METHOD VARIATIONAL PROBLEMS AND FUNCTIONAL INTEGRALS MISCELLANEOUS PART II VARIATIONAL FEATURES OF CLASSICAL CONTINUUM MODELS STATICS OF A GEOMETRICALLY LINEAR ELASTIC BODY GIBBS PRINCIPLE BOUNDEDNESS FROM BELOW COMPLEMENTARY ENERGY REISSNER VARIATIONAL PRINCIPLE PHYSICALLY LINEAR ELASTIC BODY CASTIGLIANO VARIATIONAL PRINCIPLE INTERNAL STRESSES THERMOELASTICITY DISLOCATIONS CONTINUOUSLY DISTRIBUTED DISLOCATIONS STATICS OF A GEOMETRICALLY NONLINEAR ELASTIC BODY ENERGY FUNCTIONAL DUAL VARIATIONAL PRINCIPLE PHASE EQUILIBRIUM OF ELASTIC BODIES DYNAMICS OF ELASTIC BODIES LEAST ACTION VS STATIONARY ACTION NONLINEAR EIGENVIBRATIONS LINEAR VIBRATIONS: THE RAYLEIGH PRINCIPLE THE PRINCIPLE OF LEAST ACTION IN EULERIAN COORDINATES IDEAL INCOMPRESSIBLE FLUID LEAST ACTION PRINCIPLE GENERAL FEATURES OF SOLUTIONS OF MOMENTUM EQUATIONS VARIATIONAL PRINCIPLES IN EULERIAN COORDINATES POTENTIAL FLOWS VARIATIONAL FEATURES OF KINETIC ENERGY IN VORTEX FLOWS DYNAMICS OF VORTEX LINES QUASI-TWO-DIMENSIONAL AND TWO-DIMENSIONAL VORTEX FLOWS DYNAMICS OF VORTEX FILAMENTS IN UNBOUNDED SPACE VORTEX SHEETS SYMMETRY OF THE ACTION FUNCTIONAL AND THE INTEGRALS OF MOTION VARIATIONAL PRINCIPLES FOR OPEN FLOWS IDEAL COMPRESSIBLE FLUID VARIATIONAL PRINCIPLES IN LAGRANGIAN COORDINATES GENERAL FEATURES OF DYNAMICS OF COMPRESSIBLE FLUID INCOMPRESSIBLE FLUID AS A LIMIT CASE OF COMPRESSIBLE FLUID STEADY MOTION OF IDEAL FLUID AND ELASTIC BODY THE KINEMATICS OF STEADY FLOW STEADY MOTION WITH IMPENETRABLE BOUNDARIES OPEN STEADY FLOWS OF IDEAL FLUID TWO-DIMENSIONAL FLOWS VARIATIONAL PRINCIPLES ON THE SET OF EQUIVORTICAL FLOWS REGULARIZATION OF FUNCTIONALS IN UNBOUNDED DOMAINS PRINCIPLE OF LEAST DISSIPATION HEAT CONDUCTION CREEPING MOTION OF VISCOUS FLUID IDEAL PLASTICITY FLUCTUATIONS AND VARIATIONS IN STEADY NON-EQUILIBRIUM PROCESSES MOTION OF RIGID BODIES IN FLUIDS MOTION OF A RIGID BODY IN CREEPING FLOW OF VISCOUS FLUID MOTION OF A BODY IN IDEAL INCOMPRESSIBLE FLUID MOTION OF A BODY IN A VISCOUS FLUID