DYNAMIC PHYSICS
11 5* ANGLE-ACTION VARIABLES FOR LIBRATION OF THE SIMPLE PENDULUM 11 6* BOHR-SOMMERFELD QUANTIZATION RULE 11 7* LIOUVILLE INTEGRABILITY AND KAM TORI 11 8* LIOUVILLE-ARNOLD THEOREM 11 9* CONSERVED QUANTITIES FROM A LAX PAIR 11 9 1* HARMONIC OSCILLATOR LAX PAIR 11 9 2* ISOSPECTRAL EVOLUTION AND CONSERVED QUANTITIES 11 9 3* TODA CHAIN: FLASCHKA’S VARIABLES AND A LAX PAIR 11 9 4* EULER-POINSOT TOP LAX PAIR: SPECTRAL PARAMETER PROBLEMS 12 HAMILTON-JACOBI EQUATION TIME-DEPENDENT HAMILTON-JACOBI EVOLUTION EQUATION 12 2* CONNECTION OF HAMILTON-JACOBI TO SCHR¨ODINGER AND EIKONAL EQUATIONS SEPARATION OF VARIABLES IN THE HAMILTON-JACOBI EQUATION HAMILTON’S PRINCIPAL FUNCTION AS ACTION ALONG A TRAJECTORY 12 5* GEOMETRIC INTERPRETATION OF HAMILTON-JACOBI EQUATION 13 NORMAL MODES OF OSCILLATION AND LINEAR STABILITY ELEMENTARY EXAMPLES OF COUPLED SMALL OSCILLATIONS NORMAL MODES OF TWO WEAKLY COUPLED PENDULA NORMAL MODES OF A DIATOMIC MOLECULE DOUBLE PENDULUM: FORMULATION AND SMALL OSCILLATIONS ENERGY, LAGRANGIAN AND EQUATIONS OF MOTION NORMAL MODES OF A DOUBLE PENDULUM 13 3* NORMAL MODES AROUND A STATIC EQUILIBRIUM: GENERAL FRAMEWORK SMALL PERTURBATIONS AROUND A PERIODIC SOLUTION FORMULATION AS A SYSTEM OF ?RST ORDER EQUATIONS 13 4 2* TIME EVOLUTION MATRIX 13 4 3* MONODROMY MATRIX 13 4 4* STABILITY OF A PERIODIC SOLUTION 13 4 5* KAPITZA PENDULUM WITH OSCILLATING SUPPORT: MATHIEU EQUATION 14 BIFURCATIONS: QUALITATIVE CHANGES IN DYNAMICS BIFURCATIONS OF VECTOR ?ELDS ON THE REAL LINE 14 1 1* SADDLE-NODE BIFURCATION 14 1 2* TRANSCRITICAL BIFURCATION 14 1 3* PITCHFORK BIFURCATIONS 14 1 3 1* SUPERCRITICAL PITCHFORK BIFURCATION 14 1 3 2* SUBCRITICAL PITCHFORK BIFURCATION BIFURCATIONS IN TWO DIMENSIONS 14 2 1* SADDLE-NODE, TRANSCRITICAL AND PITCHFORK BIFURCATIONS 14 2 2* HOPF BIFURCATIONS 15 FROM REGULAR TO CHAOTIC MOTION CHAOS IN ITERATIONS OF A MAP LYAPUNOV EXPONENT AND SENSITIVITY TO INITIAL CONDITIONS CHIRIKOV-TAYLOR STANDARD MAP: A KICKED ROTOR LOGISTIC MAP: PERIOD DOUBLING, CANTOR DUST AND LYAPUNOV EXPONENT 15 2* LYAPUNOV EXPONENTS FOR CONTINUOUS-TIME DYNAMICAL SYSTEMS 15 3* POINCAR´E RETURN MAP AND HOMOCLINIC TANGLE HAMILTONIAN CHAOS: ORDER-CHAOS-ORDER TRANSITION IN A DOUBLE PENDULUM 15 4 1* POINCAR´E SECTIONS AND ONSET OF CHAOS 15 4 2* RETURN TO REGULARITY AT HIGH ENERGIES 15 4 3* UNDERSTANDING THE ZERO GRAVITY DOUBLE PENDULUM 15 5* CHAOS IN LORENZ’S MODEL FOR CONVECTION 16 DYNAMICS OF CONTINUOUS DEFORMABLE MEDIA 17 VIBRATIONS OF A STRETCHED STRING AND THE WAVE EQUATION WAVE EQUATION FOR TRANSVERSE VIBRATIONS OF A STRETCHED STRING FINITE DIFFERENCES: WAVE EQUATION AS A SYSTEM OF ODES NORMAL MODES AND SOLUTION BY FOURIER SERIES RIGHT- AND LEFT-MOVING WAVES AND D’ALEMBERT’S SOLUTION CONSERVED ENERGY OF SMALL OSCILLATIONS OF A STRETCHED STRING THREE LOCAL CONSERVATION LAWS FOR THE WAVE EQUATION LAGRANGIAN AND HAMILTONIAN FOR STRETCHED STRING CONSERVED QUANTITIES FROM NOETHER’S THEOREM DISPERSION RELATION, PHASE AND GROUP VELOCITIES 17 10* LAX PAIR FOR THE ?RST ORDER WAVE EQUATION 18 HEAT DIFFUSION EQUATION AND BROWNIAN MOTION OBTAINING THE HEAT EQUATION AND ITS BASIC PROPERTIES SOLUTION OF INITIAL VALUE PROBLEM ON AN INTERVAL BY FOURIER’S SERIES 18 3* HEAT KERNEL: TIME EVOLUTION OPERATOR FOR HEAT EQUATION FROM BROWNIAN MOTION TO THE DIFFUSION EQUATION BROWNIAN MOTION AND THE ATOMIC HYPOTHESIS 18 4 2* RANDOM WALK MODEL AND THE DIFFUSION EQUATION 19 INTRODUCTION TO ?UID MECHANICS FLUID ELEMENT, LOCAL THERMAL EQUILIBRIUM AND DYNAMICAL ?ELDS FLUID STATICS: AERO- OR HYDROSTATICS FLOW VISUALIZATION: STREAMLINES, STREAKLINES AND PATHLINES MATERIAL DERIVATIVE COMPRESSIBILITY, INCOMPRESSIBILITY AND DIVERGENCE OF VELOCITY ?ELD LOCAL CONSERVATION OF MASS: CONTINUITY EQUATION EULER EQUATION FOR INVISCID ?OW IDEAL ADIABATIC ?OW: ENTROPY ADVECTION AND EQUATION OF STATE