AN ELEMENTARY TREATISE ON DYNAMICS
CONTENTS VECTOR ANALYSIS IN CARTESIAN COORDINATES INTRODUCTION OPERATIONS WITH VECTORS VECTOR OPERATORS CHANGE OF BASIS PROPOSED EXERCISES FURTHER READING VECTOR ANALYSIS IN CURVILINEAR COORDINATES CYLINDRICAL AND POLAR COORDINATES SPHERICAL COORDINATES KINEMATICS VELOCITY AND ACCELERATION FRENET EQUATIONS NEWTON’S LAWS, DYNAMICS AND GALILEAN RELATIVITY NEWTON’S LAWS CONSERVATIVE AND CENTRAL FORCES GRAVITATIONAL POTENTIAL FORCE, ENERGY, WORK, AND ENERGY CONSERVATION CONSERVATIVE FORCES CONSERVATIVE AND NON-CONSERVATIVE FORCES ANGULAR MOMENTUM, TORQUE AND CONSERVATION GALILEAN RELATIVITY AND INERTIAL REFERENCE FRAMES SYSTEMS OF PARTICLES AND VARIABLE MASS POINT-LIKE PARTICLE SYSTEMS VARIABLE MASS SYSTEMS ONE-DIMENSIONAL POTENTIALS AND TWO-DIMENSIONAL CENTRAL POTENTIALS ONE-DIMENSIONAL POTENTIALS CENTRAL POTENTIALS THE TWO-BODY PROBLEM KEPLER’S POTENTIAL NON RELATIVISTIC COLLISIONS FRONTAL COLLISIONS ELASTIC COLLISIONS IN THE CENTER OF MASS ELASTIC COLLISIONS IN THE LABORATORY FRAME RELATING BOTH FRAMES INELASTIC COLLISIONS SCATTERING BY A HARD SPHERE SCATTERING BY A REPULSIVE POTENTIAL CONTINUOUS MASS DISTRIBUTIONS GRAVITATIONAL POTENTIAL AND FIELD POTENTIALS WITH SPHERICAL SYMMETRY GRAVITATIONAL FIELD AND GAUSS’S LAW GAUSS’S LAW FOR SPHERICAL MASS DISTRIBUTIONS NON-INERTIAL REFERENCE SYSTEMS VELOCITY AND ANGULAR VELOCITY THE HEURISTIC APPROACH MOTION OVER THE EARTH’S SURFACE FREE FALL FOUCAULT’S PENDULUM RIGID BODY DYNAMICS DISCRETE CASE PRINCIPAL AXES HUYGENS–STEINER THEOREM CONTINUUM GENERALIZATION STABLE SOLUTIONS FOR THE TORQUE-FREE MOTION EARTH’S PRECESSION FREE SYMMETRIC SPINNING TOP HEAVY SYMMETRIC SPINNING TOP SPECIAL THEORY OF RELATIVITY LORENTZ–POINCARÉ TRANSFORMATIONS VELOCITY ADDITION RULES MINKOWSKI SPACE-TIME AND FOUR-VECTORS COVARIANT AND CONTRAVARIANT TRANSFORMATIONS SUMMARY FOUR-VELOCITY, ACCELERATION AND FORCE MASSLESS PARTICLES FINAL COMMENTS RELATIVISTIC COLLISIONS AND DECAYS CONSERVATION LAWS AND KINEMATIC INVARIANTS DECAYS 2 ! 2 FRONTAL COLLISIONS NON-RELATIVISTIC LAGRANGIAN AND HAMILTONIAN MECHANICS LAGRANGIAN FORMALISM CYCLIC COORDINATES AND CONSTANTS OF MOTION LAGRANGIAN WITH BOUNDARY CONDITIONS HAMILTONIAN FORMALISM STATIONARY ACTION PRINCIPLE NOETHER’S THEOREM SYMMETRIES AND CONSERVATION TIME TRANSLATIONS SPATIAL TRANSLATIONS ROTATIONS GALILEAN TRANSFORMATIONS