|
|
xi | |
Acknowledgments |
|
xv | |
Foreword |
|
xvii | |
Prologue |
|
xxiii | |
|
|
1 | (6) |
|
|
1 | (1) |
|
1.2 Multiple Star Systems |
|
|
2 | (1) |
|
|
2 | (1) |
|
1.4 Supermassive Black Holes |
|
|
3 | (1) |
|
1.5 The Cast of Characters |
|
|
4 | (3) |
|
|
7 | (28) |
|
|
7 | (3) |
|
|
10 | (4) |
|
|
14 | (9) |
|
2.4 The General N-Body Problem |
|
|
23 | (2) |
|
|
25 | (10) |
|
|
35 | (12) |
|
3.1 Choosing a Programming Language |
|
|
35 | (4) |
|
3.2 Forward Euler Integrator |
|
|
39 | (8) |
|
4 Accuracy And Performance Of The Integration |
|
|
47 | (16) |
|
|
48 | (5) |
|
4.2 Speeding Up the Code: Allocating Arrays |
|
|
53 | (4) |
|
4.3 Checking the Conservation Laws |
|
|
57 | (6) |
|
5 Fixed Step-Size Integration |
|
|
63 | (22) |
|
5.1 Truncation and Round-Off Errors |
|
|
63 | (3) |
|
|
66 | (5) |
|
|
71 | (2) |
|
|
73 | (3) |
|
5.5 Symplectic Integrators |
|
|
76 | (4) |
|
5.6 Numerical Performance |
|
|
80 | (5) |
|
6 Variable Step-Size Integration |
|
|
85 | (20) |
|
6.1 Estimating the Local Truncation Error |
|
|
86 | (3) |
|
|
89 | (3) |
|
|
92 | (2) |
|
6.4 Implementing Flexibility |
|
|
94 | (2) |
|
6.5 Numerical Performance |
|
|
96 | (3) |
|
6.6 Thoughts on Choosing the Integration Method |
|
|
99 | (1) |
|
|
100 | (5) |
|
7 The Three- And N-Body Problems |
|
|
105 | (18) |
|
7.1 From the Two-Body to the Three-Body Problem |
|
|
105 | (8) |
|
|
113 | (10) |
|
8 Gauss--Radau Integrator Of The Fifteenth Order |
|
|
123 | (40) |
|
8.1 Preparing the Second-Order System |
|
|
124 | (1) |
|
8.2 Numerical Quadratures: Choosing the Right Sequence |
|
|
125 | (5) |
|
8.3 Approximating the Integrand Using a Polynomial |
|
|
130 | (2) |
|
8.4 Approximating the Force Function |
|
|
132 | (2) |
|
8.5 Computing the Coefficients |
|
|
134 | (3) |
|
8.6 Radau Sequence and Integration Order |
|
|
137 | (2) |
|
8.7 Coding the Main Components of the Integrator |
|
|
139 | (3) |
|
8.8 Advancing One Integration Step |
|
|
142 | (5) |
|
8.9 The Complete Integrator |
|
|
147 | (4) |
|
8.10 Testing the Integrator |
|
|
151 | (4) |
|
|
155 | (8) |
|
9 Symplectic Map For Long-Term Integration |
|
|
163 | (32) |
|
9.1 Understanding Time Scales |
|
|
164 | (2) |
|
|
166 | (4) |
|
9.3 Wisdom--Holman Integrator |
|
|
170 | (16) |
|
9.4 Propagating the Solar System for a Million Years |
|
|
186 | (5) |
|
|
191 | (4) |
|
10 Building A Production Code |
|
|
195 | (46) |
|
10.1 An Object-Oriented Discussion |
|
|
195 | (2) |
|
10.2 Requirement Analysis: What Do We Want Our Code to Be? |
|
|
197 | (2) |
|
10.3 Constructing the Software Framework |
|
|
199 | (19) |
|
10.4 Accelerating the Code Using Native C |
|
|
218 | (23) |
|
|
241 | (6) |
|
11.1 What Project to Tackle? |
|
|
241 | (2) |
|
11.2 Circumbinary Planets |
|
|
243 | (4) |
|
12 Setting Up The Project |
|
|
247 | (16) |
|
|
247 | (8) |
|
12.2 The First Simulation |
|
|
255 | (3) |
|
12.3 Running on a Cluster |
|
|
258 | (5) |
|
13 Running And Analyzing The Simulations |
|
|
263 | (22) |
|
13.1 Problems with the Simulations |
|
|
263 | (8) |
|
13.2 A Suite of Integrations for Kepler-16 |
|
|
271 | (7) |
|
13.3 The Other Kepler Systems |
|
|
278 | (7) |
|
14 How To Write A Publishable Research Paper |
|
|
285 | (10) |
|
|
286 | (1) |
|
|
286 | (2) |
|
|
288 | (2) |
|
|
290 | (2) |
|
|
292 | (1) |
|
|
293 | (2) |
|
|
295 | (4) |
|
15.1 Physics of the N-Body Problem |
|
|
295 | (1) |
|
15.2 Programming Languages |
|
|
296 | (1) |
|
15.3 Numerical Integrators |
|
|
297 | (1) |
|
|
297 | (1) |
|
15.5 Publishing the Results |
|
|
298 | (1) |
|
|
299 | (46) |
|
A Derivation of Kepler's Third Law and the Kepler Equation |
|
|
301 | (6) |
|
|
301 | (3) |
|
A.2 Conserved Quantities in the N-Body Problem |
|
|
304 | (3) |
|
B Keplerian Propagator in Universal Variables |
|
|
307 | (8) |
|
|
308 | (1) |
|
B.2 Solving the Universal Kepler Equation |
|
|
309 | (1) |
|
|
310 | (5) |
|
C Introduction to Matrices |
|
|
315 | (4) |
|
D Derivations in the Lidov--Kozai Problem |
|
|
319 | (26) |
|
D.1 The Three-Body Hamiltonian |
|
|
319 | (4) |
|
D.2 Averaging the Hamiltonian |
|
|
323 | (8) |
|
D.3 The Equations of Motion |
|
|
331 | (7) |
|
D.4 Analytic Solutions in the Test Particle Quadrupole-Order Limit |
|
|
338 | (7) |
Bibliography |
|
345 | (4) |
Index |
|
349 | |