THE DYNAMICS OF PARTICLES AND OF RIGID, ELASTIC, AND FLUID BODIES

By JAMES WILLIAMS

CONTENTS INTRODUCTION GOVERNING EQUATIONS AND BOUNDARY CONDITIONS IN THE DYNAMICS OF A BOUNDED VOLUME OF LIQUID CONSERVATION LAWS GOVERNING EQUATIONS STRESS TENSORS, STRAIN RATES, AND THEIR LINKS MATHEMATICAL AND PHYSICAL MODELS BOUNDARY AND INITIAL CONDITIONS FORMULATION OF THE MAIN BOUNDARY-VALUE PROBLEM IN A CURVILINEAR COORDINATE SYSTEM DIRECT METHODS IN THE NONLINEAR PROBLEMS OF THE DYNAMICS OF BODIES CONTAINING LIQUIDS VARIATIONAL FORMULATION OF THE FREE-SURFACE PROBLEM OF LIQUID SLOSHING IN AN IMMOBILE BASIN MULTIMODAL METHOD FOR AN IMMOBILE BASIN MODAL EQUATIONS FOR NONCYLINDRICAL BASINS LINEAR MODAL EQUATIONS FOR AN IMMOBILE TANK BATEMAN–LUKE PRINCIPLE FOR THE NONLINEAR SLOSHING PROBLEM IN A TANK PERFORMING PRESCRIBED MOTIONS MULTIMODAL METHOD FOR A TANK PERFORMING PRESCRIBED MOTIONS EVALUATION OF THE STOKES–ZHUKOVSKY POTENTIALS BY THE VARIATIONAL METHOD RESULTING HYDRODYNAMIC FORCES AND MOMENTS NONLINEAR DYNAMIC EQUATIONS OF THE BODY–LIQUID SYSTEM HYDRODYNAMIC THEORY OF MOTIONS OF THE SHIPS TRANSPORTING LIQUIDS STATEMENT OF THE PROBLEM BATEMAN–LUKE VARIATIONAL PRINCIPLE FOR ?OATING BODIES CONTAINING TANKS ?LLED WITH LIQUIDS HYDRODYNAMIC FORCES AND MOMENTS ACTING UPON THE ?OATING RIGID BODY NONLINEAR DI?ERENTIAL EQUATIONS OF SPACE MOTIONS OF A RIGID BODY CONTAINING AN UPRIGHT CYLINDRICAL CAVITY PARTIALLY ?LLED WITH LIQUID NONLINEAR MODAL EQUATIONS OF LIQUID SLOSHING IN CYLINDRICAL VESSELS WITH CIRCULAR AND ANNULAR CROSS SECTIONS NONLINEAR MODAL EQUATIONS FOR “VISCOUS” LIQUID HYDRODYNAMIC COE?CIENTS FOR CIRCULAR CYLINDRICAL TANKS WITH NON?AT BOTTOMS HYDRODYNAMIC COE?CIENTS FOR THE UPRIGHT CYLINDRICAL TANK OF ELLIPTIC CROSS SECTION STOKES–ZHUKOVSKY POTENTIALS FOR COAXIAL CYLINDRICAL TANKS HYDRODYNAMIC PARAMETERS CONNECTED WITH MOTIONS OF THE RIGID BODY SCALAR EQUATIONS IN SOME SPECIAL CASES NONLINEAR EQUATIONS OF PERTURBED MOTION OF THE BODY CONTAINING A CYLINDRICAL CAVITY PARTIALLY ?LLED WITH LIQUID NONLINEAR MODAL EQUATIONS FOR NONCYLINDICAL AXISYMMETRIC TANKS NATURAL SLOSHING MODES FOR THE NONTRUNCATED CONICAL TANK NATURAL SLOSHING MODES FOR TRUNCATED CONICAL TANKS NONLINEAR MODAL EQUATIONS FOR NONTRUNCATED CONICAL TANKS NONLINEAR MODAL EQUATIONS FOR TRUNCATED CONICAL TANKS SPHERICAL VESSEL DERIVATION OF THE NONLINEAR EQUATIONS OF SPACE MOTIONS OF THE BODY–LIQUID SYSTEM BY THE METHOD OF PERTURBATION THEORY REDUCTION TO A SEQUENCE OF LINEAR BOUNDARY-VALUE PROBLEMS VECTOR FORM OF THE NONLINEAR EQUATIONS OF SPACE MOTIONS OF THE BODY–LIQUID SYSTEM MAIN BOUNDARY-VALUE PROBLEMS FOR AXIALLY SYMMETRIC CYLINDRICAL CAVITIES NEAR THE FREE SURFACE SCALAR FORM OF THE NONLINEAR EQUATIONS AND THEIR HYDRODYNAMIC COE?CIENTS IN SPECIAL CASES THE CASE OF AN UPRIGHT CYLINDRICAL CAVITY WITH CIRCULAR OR ANNULAR CROSS SECTION THE CASE OF CAVITIES OF COMPLEX GEOMETRIC SHAPES EQUIVALENT MECHANICAL SYSTEMS IN THE DYNAMICS OF A RIGID BODY WITH LIQUID NONLINEAR EQUATIONS OF TRANSLATIONAL MOTION OF A RIGID BODY WITH A CYLINDRICAL CAVITY PARTIALLY ?LLED WITH LIQUID EQUIVALENT MECHANICAL SYSTEMS FOR A RIGID BODY WITH LIQUID FORCED ?NITE-AMPLITUDE LIQUID SLOSHING IN MOVING VESSELS DYNAMIC STABILITY OF RESONANT LIQUID SLOSHING UNDER HORIZONTAL HARMONIC EXCITATIONS STABILITY OF FORCED AND PARAMETRIC SLOSHING IN THE SIMPLEST CASE CONSTRUCTION THE PERIODIC SOLUTIONS OF (8 2 1) BY ALTERNATIVE APPROXIMATE METHODS PERIODIC BUBNOV–GALERKIN SOLUTION OF (8 1 3) STABILITY OF PERIODIC SOLUTIONS OF (8 1 3) FORCED SLOSHING IN A VESSEL UNDER ANGULAR EXCITATIONS ANALYSIS OF THE RESPONSE CURVES FORCED LIQUID SLOSHING WITH DAMPING E?ECTS HYDRODYNAMIC FORCES 8 10 TRANSIENT SLOSHING 8 11 FORCED LIQUID SLOSHING IN A TAPERED CONICAL TANK BIBLIOGRAPHY