THE THREE-BODY PROBLEM
CONTENTS ASTROPHYSICS AND THE THREE-BODY PROBLEM ABOUT THE THREE-BODY PROBLEM THE THREE-BODY PROBLEM IN ASTROPHYSICS SHORT PERIOD COMETS BINARY STARS GROUPS OF GALAXIES BINARY BLACK HOLES NEWTONIAN MECHANICS NEWTON’S LAWS INERTIAL COORDINATE SYSTEM EQUATIONS OF MOTION FOR N BODIES GRAVITATIONAL POTENTIAL CONSTANTS OF MOTION THE VIRIAL THEOREM THE LAGRANGE AND JACOBI FORMS OF THE EQUATIONS OF MOTION CONSTANTS OF MOTION IN THE THREE-BODY PROBLEM MOMENT OF INERTIA SCALING OF THE THREE-BODY PROBLEM INTEGRATION OF ORBITS DIMENSIONS AND UNITS OF THE THREE-BODY PROBLEM CHAOS IN THE THREE-BODY PROBLEM ROTATING COORDINATE SYSTEM PROBLEMS THE TWO-BODY PROBLEM EQUATIONS OF MOTION CENTRE OF MASS COORDINATE SYSTEM INTEGRALS OF THE EQUATION OF MOTION EQUATION OF THE ORBIT AND KEPLER’S ?RST LAW KEPLER’S SECOND LAW ORBITAL ELEMENTS ORBITAL VELOCITY TRUE AND ECCENTRIC ANOMALIES MEAN ANOMALY AND KEPLER’S EQUATION SOLUTION OF KEPLER’S EQUATION KEPLER’S THIRD LAW POSITION AND SPEED AS FUNCTIONS OF ECCENTRIC ANOMALY HYPERBOLIC ORBIT DYNAMICAL FRICTION SERIES EXPANSIONS HAMILTONIAN MECHANICS GENERALISED COORDINATES HAMILTONIAN PRINCIPLE VARIATIONAL CALCULUS LAGRANGIAN EQUATIONS OF MOTION HAMILTONIAN EQUATIONS OF MOTION PROPERTIES OF THE HAMILTONIAN CANONICAL TRANSFORMATIONS EXAMPLES OF CANONICAL TRANSFORMATIONS THE HAMILTON–JACOBI EQUATION TWO-BODY PROBLEM IN HAMILTONIAN MECHANICS: TWO DIMENSIONS TWO-BODY PROBLEM IN HAMILTONIAN MECHANICS: THREE DIMENSIONS DELAUNAY’S ELEMENTS HAMILTONIAN FORMULATION OF THE THREE-BODY PROBLEM ELIMINATION OF NODES ELIMINATION OF MEAN ANOMALIES THE PLANAR RESTRICTED CIRCULAR THREE-BODY PROBLEM AND OTHER SPECIAL CASES COORDINATE FRAMES JACOBIAN INTEGRAL LAGRANGIAN POINTS STABILITY OF THE LAGRANGIAN POINTS SATELLITE ORBITS THE LAGRANGIAN EQUILATERAL TRIANGLE ONE-DIMENSIONAL THREE-BODY PROBLEM THREE-BODY SCATTERING SCATTERING OF SMALL FAST BODIES FROM A BINARY EVOLUTION OF THE SEMI-MAJOR AXIS AND ECCENTRICITY CAPTURE OF SMALL BODIES BY A CIRCULAR BINARY ORBITAL CHANGES IN ENCOUNTERS WITH PLANETS INCLINATION AND PERIHELION DISTANCE LARGE ANGLE SCATTERING CHANGES IN THE ORBITAL ELEMENTS CHANGES IN THE RELATIVE ORBITAL ENERGY OF THE BINARY ESCAPE IN THE GENERAL THREE-BODY PROBLEM ESCAPES IN A BOUND THREE-BODY SYSTEM A PLANAR CASE ESCAPE VELOCITY ESCAPER MASS ANGULAR MOMENTUM ESCAPE ANGLE SCATTERING AND CAPTURE IN THE GENERAL PROBLEM CAPTURE EJECTIONS AND LIFETIME EXCHANGE AND ?YBY RATES OF CHANGE OF THE BINDING ENERGY COLLISIONS PERTURBATIONS IN HIERARCHICAL SYSTEMS OSCULATING ELEMENTS LAGRANGIAN PLANETARY EQUATIONS THREE-BODY PERTURBING FUNCTION DOUBLY ORBIT-AVERAGED PERTURBING FUNCTION MOTIONS IN THE HIERARCHICAL THREE-BODY PROBLEM PERTURBATIONS IN STRONG THREE-BODY ENCOUNTERS PERTURBATIONS OF THE INTEGRALS K AND E BINARY EVOLUTION WITH A CONSTANT PERTURBING FORCE SLOW ENCOUNTERS INCLINATION DEPENDENCE CHANGE IN ECCENTRICITY STABILITY OF TRIPLE SYSTEMS FAST ENCOUNTERS AVERAGE ENERGY EXCHANGE SOME ASTROPHYSICAL PROBLEMS BINARY BLACK HOLES IN CENTRES OF GALAXIES THE PROBLEM OF THREE BLACK HOLES SATELLITE BLACK HOLE SYSTEMS THREE GALAXIES BINARY STARS IN THE GALAXY EVOLUTION OF COMET ORBITS REFERENCES