THE ELEMENTS OF DYNAMICS (MECHANICS)

By BARBARA RODRIGUEZ

CONTENTS DIMENSIONS AND UNITS FUNDAMENTAL CONCEPTS BASE UNITS AND DIMENSIONS DIMENSIONS OF COMMON PHYSICAL QUANTITIES THE BUCKINGHAM PI THEOREM ABSOLUTE ERRORS, RELATIVE ERRORS, AND UNITS UNITS AND COMPUTERS UNIT SYSTEMS EXAMPLE ON CHALLENGES ARISING FROM UNIT SYSTEMS PHYSICALQUANTITY: A TOOL FOR COMPUTING WITH UNITS PARAMPOOL: USER INTERFACES WITH AUTOMATIC UNIT CONVERSION POOL OF PARAMETERS FETCHING POOL DATA FOR COMPUTING READING COMMAND-LINE OPTIONS SETTING DEFAULT VALUES IN A ?LE SPECIFYING MULTIPLE VALUES OF INPUT PARAMETERS GENERATING A GRAPHICAL USER INTERFACE ORDINARY DI?ERENTIAL EQUATION MODELS EXPONENTIAL DECAY PROBLEMS FUNDAMENTAL IDEAS OF SCALING THE BASIC MODEL PROBLEM THE TECHNICAL STEPS OF THE SCALING PROCEDURE MAKING SOFTWARE FOR UTILIZING THE SCALED MODEL SCALING A GENERALIZED PROBLEM VARIABLE COE?CIENTS SCALING A COOLING PROBLEM WITH CONSTANT TEMPERATURE IN THE SURROUNDINGS SCALING A COOLING PROBLEM WITH TIME-DEPENDENT SURROUNDINGS SCALING A NONLINEAR ODE 2 1 10 SIR ODE SYSTEM FOR SPREADING OF DISEASES 2 1 11 SIRV MODEL WITH ?NITE IMMUNITY 2 1 12 MICHAELIS-MENTEN KINETICS FOR BIOCHEMICAL REACTIONS VIBRATION PROBLEMS UNDAMPED VIBRATIONS WITHOUT FORCING UNDAMPED VIBRATIONS WITH CONSTANT FORCING UNDAMPED VIBRATIONS WITH TIME-DEPENDENT FORCING DAMPED VIBRATIONS WITH FORCING OSCILLATING ELECTRIC CIRCUITS BASIC PARTIAL DI?ERENTIAL EQUATION MODELS THE WAVE EQUATION HOMOGENEOUS DIRICHLET CONDITIONS IN 1D IMPLEMENTATION OF THE SCALED WAVE EQUATION TIME-DEPENDENT DIRICHLET CONDITION VELOCITY INITIAL CONDITION VARIABLE WAVE VELOCITY AND FORCING DAMPED WAVE EQUATION A THREE-DIMENSIONAL WAVE EQUATION PROBLEM THE DI?USION EQUATION HOMOGENEOUS 1D DI?USION EQUATION GENERALIZED DI?USION PDE JUMP BOUNDARY CONDITION OSCILLATING DIRICHLET CONDITION REACTION-DI?USION EQUATIONS FISHER’S EQUATION NONLINEAR REACTION-DI?USION PDE THE CONVECTION-DI?USION EQUATION CONVECTION-DI?USION WITHOUT A FORCE TERM STATIONARY PDE CONVECTION-DI?USION WITH A SOURCE TERM ADVANCED PARTIAL DI?ERENTIAL EQUATION MODELS THE EQUATIONS OF LINEAR ELASTICITY THE GENERAL TIME-DEPENDENT ELASTICITY PROBLEM DIMENSIONLESS STRESS TENSOR WHEN CAN THE ACCELERATION TERM BE NEGLECTED? THE STATIONARY ELASTICITY PROBLEM QUASI-STATIC THERMO-ELASTICITY THE NAVIER-STOKES EQUATIONS THE MOMENTUM EQUATION WITHOUT BODY FORCES SCALING OF TIME FOR LOW REYNOLDS NUMBERS SHEAR STRESS AS PRESSURE SCALE GRAVITY FORCE AND THE FROUDE NUMBER OSCILLATING BOUNDARY CONDITIONS AND THE STROUHAL NUMBER CAVITATION AND THE EULER NUMBER FREE SURFACE CONDITIONS AND THE WEBER NUMBER THERMAL CONVECTION FORCED CONVECTION FREE CONVECTION THE GRASHOF, PRANDTL, AND ECKERT NUMBERS HEAT TRANSFER AT BOUNDARIES AND THE NUSSELT AND BIOT NUMBERS COMPRESSIBLE GAS DYNAMICS THE EULER EQUATIONS OF GAS DYNAMICS GENERAL ISENTROPIC ?OW THE ACOUSTIC APPROXIMATION FOR SOUND WAVES WATER SURFACE WAVES DRIVEN BY GRAVITY THE MATHEMATICAL MODEL SCALING WAVES IN DEEP WATER LONG WAVES IN SHALLOW WATER TWO-PHASE POROUS MEDIA ?OW REFERENCES