Introduction | p. 1 |
Definitions and Properties | p. 5 |
Notations | p. 5 |
The Restricted Problem: Equations | p. 5 |
Periodic Solutions and Periodic Orbits | p. 6 |
The Period-in-Family | p. 8 |
Structure of Families | p. 9 |
Family Segments | p. 12 |
Symmetry | p. 12 |
Stability | p. 13 |
Generating Orbits and Keplerian Orbits | p. 14 |
Species | p. 16 |
Generating Orbits of the First Species | p. 21 |
Kinds | p. 21 |
First Kind | p. 22 |
The Case n = 1 | p. 22 |
The Case n &neq; 1 | p. 23 |
Second Kind | p. 24 |
Symmetric Orbits | p. 26 |
Asymmetric Orbits | p. 31 |
Summary | p. 33 |
Generating Orbits of the Second Species | p. 35 |
Arcs | p. 35 |
Supporting Ellipses and Types | p. 38 |
Type 1 | p. 41 |
S-Arcs | p. 42 |
The (A, Z) Plane | p. 48 |
S-Arc Families | p. 52 |
T-Arcs and T-Arc Families | p. 55 |
Overview | p. 59 |
Types 2, 3, 4 | p. 59 |
Ends of S- and T-Arc Families | p. 62 |
Extremums of C: Arc Family Segments | p. 68 |
Orbits | p. 73 |
Second Species Families | p. 75 |
Ends of Family Segments | p. 76 |
Generating Orbits of the Third Species | p. 79 |
¿-Generating Orbits | p. 79 |
Continuation from ¿ = 0 to ¿ > 0 | p. 82 |
First Species | p. 82 |
Second Species | p. 82 |
¿-Generating Orbits for 0 < ¿ < 1/3 | p. 83 |
First Species | p. 84 |
Second Species | p. 85 |
Third Species | p. 88 |
¿-Generating Orbits for ¿ = 1/3 | p. 88 |
Continuation from ¿ < 1/3 to ¿ = 1/3 | p. 91 |
Family f | p. 91 |
Family a | p. 91 |
Family c | p. 92 |
Family g' | p. 92 |
Family g | p. 92 |
Recapitulation | p. 92 |
Other Families | p. 93 |
¿-Generating Orbits for ¿ > 1/3 | p. 93 |
Continuation from ¿ = 1/3 to ¿ > 1/3 | p. 94 |
Conclusions | p. 94 |
Bifurcation Orbits | p. 95 |
First Species and First Species | p. 96 |
First Kind and First Kind | p. 96 |
First Kind and Second Kind, Symmetric | p. 96 |
First Kind and Second Kind, Asymmetric | p. 97 |
Second Kind, Symmetric and Symmetric | p. 97 |
Second Kind, Symmetric and Asymmetric | p. 97 |
Second Kind, Asymmetric and Asymmetric | p. 97 |
Second Species and First or Second Species | p. 98 |
Total Bifurcation | p. 99 |
Partial Bifurcation | p. 115 |
Third Species and First or Second Species | p. 123 |
Third Species and Third Species | p. 123 |
Recapitulation | p. 123 |
Junctions: Symmetry | p. 125 |
First Species Bifurcations | p. 125 |
Third Species Bifurcations | p. 126 |
Second Species Bifurcations | p. 126 |
Partial Bifurcation | p. 127 |
Total Bifurcation | p. 128 |
Conclusions | p. 134 |
Junctions: Broucke's Principle | p. 137 |
Definition | p. 137 |
Side of Passage for a Node | p. 139 |
Type 1 | p. 140 |
Type 2 | p. 143 |
Type 3 | p. 145 |
Side of Passage for an Antinode | p. 147 |
Type 1 | p. 147 |
Type 2 | p. 150 |
Type 3 | p. 151 |
Results: Partial Bifurcation | p. 152 |
Type 1 | p. 152 |
Type 2 | p. 160 |
Type 3 | p. 162 |
Results: Total Bifurcation | p. 162 |
Type 1 | p. 162 |
Type 2 | p. 167 |
Type 3 | p. 167 |
Recapitulation | p. 167 |
Fragments | p. 171 |
Introduction | p. 171 |
Accidents | p. 172 |
Explanation of the Fragment Tables | p. 173 |
First Species Family Segments | p. 174 |
First Kind: Retrograde Orbits | p. 174 |
First Kind: Direct Orbits | p. 174 |
Second Kind | p. 175 |
Second Species Family Segments | p. 179 |
Detection of Bifurcation Orbits | p. 179 |
Data on Arc Family Segments | p. 183 |
Fragments | p. 190 |
Third Species Family Segments | p. 196 |
Generating Families | p. 203 |
Algorithm | p. 203 |
Explanation of the Tables | p. 205 |
Natural Families | p. 206 |
Family a | p. 207 |
Family b | p. 208 |
Family c | p. 209 |
Family f | p. 209 |
Family g | p. 210 |
Family h | p. 211 |
Family i | p. 213 |
Family l | p. 214 |
Family m | p. 214 |
Summary | p. 214 |
Other Families | p. 214 |
Comparison with Computed Families | p. 220 |
Family a | p. 221 |
Family b | p. 223 |
Family c | p. 224 |
Family f | p. 225 |
Family g | p. 225 |
Family h | p. 225 |
Family i | p. 225 |
Families l and m | p. 229 |
Final Comments | p. 232 |
Correspondence Between Old and New Notations | p. 235 |
Arcs | p. 235 |
Arc Families | p. 237 |
Critical Arcs | p. 240 |
The Domain D2 | p. 243 |
The Curved Boundary ¿ | p. 243 |
S-Arc Families in Domain D2 | p. 245 |
Number of Branches | p. 251 |
Partial Bifurcation | p. 251 |
Type 1 | p. 251 |
Type 2 | p. 253 |
Type 3 | p. 254 |
Total Bifurcation | p. 255 |
Type 1 | p. 256 |
Type 2 | p. 258 |
Type 3 | p. 260 |
Conclusions | p. 264 |
Index of Definitions | p. 265 |
Index of Notations | p. 269 |
References | p. 275 |
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