AN ELEMENTARY TREATISE ON THE DYNAMICS OF A PARTICLE AND OF RIGID BODIES

By S. BEENR

CONTENTS PART I NEWTONIAN MECHANICS IN MOVING COORDINATE SYSTEMS NEWTON’S EQUATIONS IN A ROTATING COORDINATE SYSTEM INTRODUCTION OF THE OPERATOR D FORMULATION OF NEWTON’S EQUATION IN THE ROTATING COORDINATE SYSTEM NEWTON’S EQUATIONS IN SYSTEMS WITH ARBITRARY RELATIVE MOTION FREE FALL ON THE ROTATING EARTH PERTURBATION CALCULATION METHOD OF SUCCESSIVE APPROXIMATION EXACT SOLUTION FOUCAULT’S PENDULUM SOLUTION OF THE DIFFERENTIAL EQUATIONS DISCUSSION OF THE SOLUTION PART II MECHANICS OF PARTICLE SYSTEMS DEGREES OF FREEDOM DEGREES OF FREEDOM OF A RIGID BODY CENTER OF GRAVITY MECHANICAL FUNDAMENTAL QUANTITIES OF SYSTEMS OF MASS POINTS LINEAR MOMENTUM OF THE MANY-BODY SYSTEM ANGULAR MOMENTUM OF THE MANY-BODY SYSTEM ENERGY LAW OF THE MANY-BODY SYSTEM TRANSFORMATION TO CENTER-OF-MASS COORDINATES TRANSFORMATION OF THE KINETIC ENERGY PART III VIBRATING SYSTEMS VIBRATIONS OF COUPLED MASS POINTS THE VIBRATING CHAIN THE VIBRATING STRING SOLUTION OF THE WAVE EQUATION NORMAL VIBRATIONS FOURIER SERIES 10 THE VIBRATING MEMBRANE DERIVATION OF THE DIFFERENTIAL EQUATION SOLUTION OF THE DIFFERENTIAL EQUATION INCLUSION OF THE BOUNDARY CONDITIONS EIGENFREQUENCIES DEGENERACY NODAL LINES GENERAL SOLUTION SUPERPOSITION OF NODE LINE FIGURES THE CIRCULAR MEMBRANE 10 10 SOLUTION OF BESSEL’S DIFFERENTIAL EQUATION PART IV MECHANICS OF RIGID BODIES 11 ROTATION ABOUT A FIXED AXIS MOMENT OF INERTIA THE PHYSICAL PENDULUM 12 ROTATION ABOUT A POINT TENSOR OF INERTIA KINETIC ENERGY OF A ROTATING RIGID BODY THE PRINCIPAL AXES OF INERTIA EXISTENCE AND ORTHOGONALITY OF THE PRINCIPAL AXES TRANSFORMATION OF THE TENSOR OF INERTIA TENSOR OF INERTIA IN THE SYSTEM OF PRINCIPAL AXES ELLIPSOID OF INERTIA 13 THEORY OF THE TOP THE FREE TOP GEOMETRICAL THEORY OF THE TOP ANALYTICAL THEORY OF THE FREE TOP THE HEAVY SYMMETRIC TOP: ELEMENTARY CONSIDERATIONS FURTHER APPLICATIONS OF THE TOP THE EULER ANGLES MOTION OF THE HEAVY SYMMETRIC TOP PART V LAGRANGE EQUATIONS 14 GENERALIZED COORDINATES QUANTITIES OF MECHANICS IN GENERALIZED COORDINATES 15 D’ALEMBERT PRINCIPLE AND DERIVATION OF THE LAGRANGE EQUATIONS VIRTUAL DISPLACEMENTS 16 LAGRANGE EQUATION FOR NONHOLONOMIC CONSTRAINTS 17 SPECIAL PROBLEMS VELOCITY-DEPENDENT POTENTIALS NONCONSERVATIVE FORCES AND DISSIPATION FUNCTION (FRICTION FUNCTION) NONHOLONOMIC SYSTEMS AND LAGRANGE MULTIPLIERS PART VI HAMILTONIAN THEORY 18 HAMILTON’S EQUATIONS THE HAMILTON PRINCIPLE GENERAL DISCUSSION OF VARIATIONAL PRINCIPLES PHASE SPACE AND LIOUVILLE’S THEOREM THE PRINCIPLE OF STOCHASTIC COOLING 19 CANONICAL TRANSFORMATIONS 20 HAMILTON–JACOBI THEORY VISUAL INTERPRETATION OF THE ACTION FUNCTION S TRANSITION TO QUANTUM MECHANICS 21 EXTENDED HAMILTON–LAGRANGE FORMALISM EXTENDED SET OF EULER–LAGRANGE EQUATIONS EXTENDED SET OF CANONICAL EQUATIONS EXTENDED CANONICAL TRANSFORMATIONS 22 EXTENDED HAMILTON–JACOBI EQUATION PART VII NONLINEAR DYNAMICS 23 DYNAMICAL SYSTEMS DISSIPATIVE SYSTEMS: CONTRACTION OF THE PHASE-SPACE VOLUME ATTRACTORS EQUILIBRIUM SOLUTIONS LIMIT CYCLES 24 STABILITY OF TIME-DEPENDENT PATHS PERIODIC SOLUTIONS DISCRETIZATION AND POINCARÉ CUTS 25 BIFURCATIONS STATIC BIFURCATIONS BIFURCATIONS OF TIME-DEPENDENT SOLUTIONS 26 LYAPUNOV EXPONENTS AND CHAOS ONE-DIMENSIONAL SYSTEMS MULTIDIMENSIONAL SYSTEMS STRETCHING AND FOLDING IN PHASE SPACE FRACTAL GEOMETRY 27 SYSTEMS WITH CHAOTIC DYNAMICS DYNAMICS OF DISCRETE SYSTEMS ONE-DIMENSIONAL MAPPINGS PART VIII ON THE HISTORY OF MECHANICS 28 EMERGENCE OF OCCIDENTAL PHYSICS IN THE SEVENTEENTH CENTURY NOTES RECOMMENDATIONS FOR FURTHER READING ON THEORETICAL MECHANICS