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Singularities, Collisions and Regularization Theory |
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1 | (24) |
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1 | (2) |
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3 | (1) |
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Past and future collisions in the Solar System |
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4 | (5) |
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9 | (8) |
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Triple collisions and central configurations |
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17 | (1) |
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Chaotic diffusion: the inclined billiard |
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18 | (2) |
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Noncollision singularities |
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20 | (5) |
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23 | (2) |
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The Levi--Civita, KS and Radial--Inversion Regularizing Transformations |
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25 | (24) |
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25 | (1) |
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The two- and three-body problem |
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26 | (3) |
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26 | (1) |
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The planar, circular, restricted three-body problem |
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26 | (3) |
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The Levi--Civita regularization |
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29 | (7) |
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29 | (3) |
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The planar, circular, restricted three-body problem |
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32 | (4) |
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The Kustaanheimo--Stiefel regularization |
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36 | (8) |
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The Kustaanheimo--Stiefel transformation |
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36 | (3) |
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Canonicity of the KS-transformation |
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39 | (5) |
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The radial--inversion transformation |
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44 | (5) |
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48 | (1) |
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The Birkhoff and B3 Regularizing Transformations |
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49 | (14) |
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Maria Gabriella Della Penna |
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49 | (1) |
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The Birkhoff regularization |
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49 | (8) |
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57 | (3) |
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60 | (3) |
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62 | (1) |
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Perturbative Methods in Regularization Theory |
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63 | (9) |
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63 | (1) |
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63 | (4) |
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64 | (1) |
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64 | (1) |
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The generalized eccentric anomaly case |
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65 | (2) |
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Analytic perturbative methods |
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67 | (5) |
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Hamilton--Jacobi for the fictitious-time case |
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67 | (1) |
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Hamilton--Jacobi for the generalized eccentric anomaly case |
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68 | (1) |
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69 | (1) |
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70 | (1) |
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71 | (1) |
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Collisions and Singularities in the n-body Problem |
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72 | (9) |
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72 | (1) |
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Non-collision singularities in Newtonian systems |
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72 | (3) |
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73 | (2) |
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75 | (3) |
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The example of Mather and McGehee |
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75 | (1) |
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The first example of Gerver |
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75 | (1) |
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76 | (1) |
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The second example of Gerver |
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77 | (1) |
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Multiple and simultaneous binary collisions |
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78 | (1) |
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79 | (2) |
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79 | (2) |
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Triple Collision and Close Triple Encounters |
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81 | (20) |
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81 | (5) |
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The general three-body problem: equations of motion, integrals of motion |
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82 | (1) |
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Angular momentum, Sundman's theory |
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83 | (3) |
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86 | (8) |
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Homographic and homothetic solutions |
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86 | (1) |
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87 | (3) |
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Triple collision, Siegel's series |
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90 | (4) |
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The close triple encounter |
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94 | (7) |
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95 | (1) |
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The triple-collision manifold |
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96 | (2) |
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98 | (3) |
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Dynamical and Kinetic Aspects of Collisions |
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101 | (13) |
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101 | (1) |
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101 | (1) |
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Invariants, approximate motion and collisions |
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102 | (2) |
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Collisions and Lyapunov exponents |
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104 | (1) |
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Kinetic theory and BBGKY hierarchy |
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105 | (2) |
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Mean-field limit and Vlasov equation |
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107 | (2) |
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Vlasov--Poisson equation for Coulomb and Newton interactions |
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109 | (1) |
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Boltzmann--Grad limit and Boltzmann equation |
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110 | (1) |
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Entropy dissipation for the Boltzmann equation |
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111 | (3) |
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113 | (1) |
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Chaotic Scattering in Planetary Rings |
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114 | (31) |
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114 | (1) |
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Dynamics of planetary rings |
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115 | (12) |
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115 | (1) |
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115 | (7) |
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122 | (3) |
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125 | (2) |
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127 | (5) |
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129 | (1) |
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130 | (1) |
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131 | (1) |
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132 | (1) |
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132 | (13) |
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The model and an interesting limit |
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133 | (4) |
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137 | (4) |
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141 | (3) |
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144 | (1) |
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Close Encounters in Opik's Theory |
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145 | (34) |
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145 | (1) |
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Basic formulae of Opik's theory |
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146 | (5) |
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The components of the planetocentric velocity |
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146 | (1) |
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147 | (1) |
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148 | (3) |
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From the planetocentric to the b-plane frame and back |
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151 | (3) |
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The ecliptic on the b-plane |
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152 | (1) |
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The projection of the X-axis on the b-plane |
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152 | (1) |
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The projection of the Y-axis on the b-plane |
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152 | (1) |
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The projection of the Z-axis on the b-plane |
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153 | (1) |
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153 | (1) |
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The motion of the small body |
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154 | (10) |
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The local Minimum Orbital Intersection Distance (MOID) |
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155 | (1) |
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The planetocentric orbital elements of the small body |
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156 | (1) |
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157 | (3) |
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160 | (1) |
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Post-encounter coordinates in the post-encounter b-plane |
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161 | (1) |
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162 | (2) |
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Resonant returns in Opik's theory |
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164 | (2) |
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Solving for a given final semimajor axis |
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164 | (1) |
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165 | (1) |
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The distribution of energy perturbations |
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166 | (4) |
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Energy perturbations for a given MOID |
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170 | (1) |
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Geocentric variables to characterize meteor orbits |
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170 | (9) |
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An orbital similarity criterion based on geocentric quantities |
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171 | (4) |
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Secular invariance of U and θ |
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175 | (2) |
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177 | (2) |
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Generalized Averaging Principle and Proper Elements for NEAs |
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179 | (34) |
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Giovanni-Federico Gronchi |
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179 | (1) |
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The classical averaging principle |
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180 | (3) |
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The full equations of motion |
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180 | (1) |
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181 | (2) |
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Difficulties arising with crossing orbits |
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183 | (1) |
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Generalized averaging principle in the circular coplanar case |
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183 | (16) |
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Geometry of the node crossing |
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183 | (3) |
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Description of the osculating orbits |
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186 | (1) |
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187 | (1) |
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188 | (2) |
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190 | (1) |
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191 | (3) |
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Boundedness of the remainder function |
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194 | (2) |
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The derivatives of the averaged perturbing function R |
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196 | (3) |
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199 | (4) |
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The secular evolution algorithm |
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201 | (1) |
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Different dynamical behavior of NEAs |
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202 | (1) |
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203 | (4) |
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207 | (1) |
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Generalized averaging principle in the eccentric--inclined case |
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208 | (2) |
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The mutual reference frame |
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209 | (1) |
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210 | (3) |
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210 | (3) |
| Subject Index |
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213 | |
