Astrophysics and three-body problem / 1: |
Newtonian mechanics / 2: |
Two-body problem / 3: |
Hamiltonian mechanics / 4: |
The planar restricted circular three body problem and other special cases / 5: |
Three-body scattering / 6: |
Escape in the general three body problem / 7: |
Scattering and capture in the general problem / 8: |
Perturbations in hierarchical systems / 9: |
Perurbations in strong three-body encounters / 10: |
Some astrophysical problems / 11: |
Preface |
Astrophysics and the three-body problem |
About the three-body problem / 1.1: |
The three-body problem in astrophysics / 1.2: |
Short period comets / 1.3: |
Binary stars / 1.4: |
Groups of galaxies / 1.5: |
Binary black holes / 1.6: |
Newton's laws / 2.1: |
Inertial coordinate system / 2.2: |
Equations of motion for N bodies / 2.3: |
Gravitational potential / 2.4: |
Constants of motion / 2.5: |
The virial theorem / 2.6: |
The Lagrange and Jacobi forms of the equations of motion / 2.7: |
Constants of motion in the three-body problem / 2.8: |
Moment of inertia / 2.9: |
Scaling of the three-body problem / 2.10: |
Integration of orbits / 2.11: |
Dimensions and units of the three-body problem / 2.12: |
Chaos in the three-body problem / 2.13: |
Rotating coordinate system / 2.14: |
Problems |
The two-body problem |
Equations of motion / 3.1: |
Centre of mass coordinate system / 3.2: |
Integrals of the equation of motion / 3.3: |
Equation of the orbit and Kepler's first law / 3.4: |
Kepler's second law / 3.5: |
Orbital elements / 3.6: |
Orbital velocity / 3.7: |
True and eccentric anomalies / 3.8: |
Mean anomaly and Kepler's equation / 3.9: |
Solution of Kepler's equation / 3.10: |
Kepler's third law / 3.11: |
Position and speed as functions of eccentric anomaly / 3.12: |
Hyperbolic orbit / 3.13: |
Dynamical friction / 3.14: |
Series expansions / 3.15: |
Generalised coordinates / 4.1: |
Hamiltonian principle / 4.2: |
Variational calculus / 4.3: |
Lagrangian equations of motion / 4.4: |
Hamiltonian equations of motion / 4.5: |
Properties of the Hamiltonian / 4.6: |
Canonical transformations / 4.7: |
Examples of canonical transformations / 4.8: |
The Hamilton-Jacobi equation / 4.9: |
Two-body problem in Hamiltonian mechanics: two dimensions / 4.10: |
Two-body problem in Hamiltonian mechanics: three dimensions / 4.11: |
Delaunay's elements / 4.12: |
Hamiltonian formulation of the three-body problem / 4.13: |
Elimination of nodes / 4.14: |
Elimination of mean anomalies / 4.15: |
The planar restricted circular three-body problem and other special cases |
Coordinate frames / 5.1: |
Jacobian integral / 5.2: |
Lagrangian points / 5.4: |
Stability of the Lagrangian points / 5.5: |
Satellite orbits / 5.6: |
The Lagrangian equilateral triangle / 5.7: |
One-dimensional three-body problem / 5.8: |
Scattering of small fast bodies from a binary / 6.1: |
Evolution of the semi-major axis and eccentricity / 6.2: |
Capture of small bodies by a circular binary / 6.3: |
Orbital changes in encounters with planets / 6.4: |
Inclination and perihelion distance / 6.5: |
Large angle scattering / 6.6: |
Changes in the orbital elements / 6.7: |
Changes in the relative orbital energy of the binary / 6.8: |
Escape in the general three-body problem |
Escapes in a bound three-body system / 7.1: |
A planar case / 7.2: |
Escape velocity / 7.3: |
Escaper mass / 7.4: |
Angular momentum / 7.5: |
Escape angle / 7.6: |
Capture / 8.1: |
Ejections and lifetime / 8.3: |
Exchange and flyby / 8.4: |
Rates of change of the binding energy / 8.5: |
Collisions / 8.6: |
Osculating elements / 9.1: |
Lagrangian planetary equations / 9.2: |
Three-body perturbing function / 9.3: |
Doubly orbit-averaged perturbing function / 9.4: |
Motions in the hierarchical three-body problem / 9.5: |
Perturbations in strong three-body encounters |
Perturbations of the integrals k and e / 10.1: |
Binary evolution with a constant perturbing force / 10.2: |
Slow encounters / 10.3: |
Inclination dependence / 10.4: |
Change in eccentricity / 10.5: |
Stability of triple systems / 10.6: |
Fast encounters / 10.7: |
Average energy exchange / 10.8: |
Binary black holes in centres of galaxies / 11.1: |
The problem of three black holes / 11.2: |
Satellite black hole systems / 11.3: |
Three galaxies / 11.4: |
Binary stars in the Galaxy / 11.5: |
Evolution of comet orbits / 11.6: |
References |
Author index |
Subject index |
Astrophysics and three-body problem / 1: |
Newtonian mechanics / 2: |
Two-body problem / 3: |
Hamiltonian mechanics / 4: |
The planar restricted circular three body problem and other special cases / 5: |
Three-body scattering / 6: |