The three-body problem

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The three-body problem / Mauri Valtonen and Hannu Karttunen

資料種別:

電子ブック

出版情報:

[Cambridge] : Cambridge University Press, 2009, c2010

形態:

1 online resource (x, 345 p.)

著者名:

ISBN:

9780511616006 [0511616007] (: electronic bk)

書誌ID:

EB00001318

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書誌詳細

注記:

Access: via World Wide Web
Originally printed: Cambridge : Cambridge University Press , c2005
Description based on online resource; title from PDF title page (viewed on September 12, 2022)

主題:

Three-body problem

言語:

英語

目次情報:

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：

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