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| Meyer K.R. — Periodic Solutions of the N-Body Problem |
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| Предметный указатель |
Action, free 57
Action, proper 57
Anti-symplectic 51
Aristotle 55
Bifurcation 98—100
Center of mass 10 93 101 105 112 120
Central configuration 39—41 114 129 132—133
Conservative 20
CONTINUE 3 90 96
Continue, elliptic problem 136—137
Continue, equilibrium 72 73
Continue, fixed point 74
Continue, Hill's lunar equations 125—126
Continue, lunar problem 107—109 116—117
Continue, N + 1-body problem 102
Continue, periodic solution 79 82
Continue, satellite problem 89—90
Continue, three-body problem 96—97
Coordinates, action-angle 30—32
Coordinates, Apollonius 130—132
Coordinates, canonical 21
Coordinates, central configuration 45—49
Coordinates, ignorable 38 95
Coordinates, Jacobi 25—30 87 105 111—112 120
Coordinates, polar 30—32
Coordinates, rotating 24—25 91 100 105
Coordinates, spherical 34—36
Coordinates, symplectic 20—32 106 113
Cross section 77
Cylinder theorem 82
Degrees of freedom 19
Differential equations with integrals 60—70 79—82
Differential equations, autonomous 76—79
Differential equations, autonomous, continued 79
Differential equations, autonomous, elementay solution 78
Differential equations, autonomous, multipliers 81
Differential equations, periodic 75—76
Differential equations, periodic, multipliers 75
Differential equations, periodic, stable 75
Differential equations, symmetric 82—85
Differential equations, symmetric, Hamiltonian 85
Elliptic restricted problem 17—18 129—137
Equilibrium 39 71—73 113
Equilibrium, elementary 71
Equilibrium, hyperbolic 72
Equilibrium, stable 72
Euclidean motions 52
Exponents 71 108
Fixed point 73—75
Fixed point, continued 74
Fixed point, elementary 73
Fixed point, multiplier 73
Fixed point, stable 74
Flow 20
Generating functions 22—24
| Group, action 54
Group, general linear 53
Group, isotropy 57
Group, Lie 53
Group, orthogal 53
Group, symmetry 55
Group, symplectic 53
Group, unitary 53
Hill's lunar equations 17—18 110 119—127 137
Kepler problem 1 11—12 32—34 37 49 51 61 88 97 106 112—113 122 123 130
Libration points 15
Lie algebra 58 70
Main problem, comet problem 113—115
Main problem, elliptic problem 133—135
Main problem, Hill's lunar equation 120—124
Main problem, lunar 105—107
Main problem, N + 1-bodies 100—101
Main problem, satellite 87—89
Main problem, three-bodies 92—96
Manifold 53
Meyer, Karl 98
Moment of inertia 40 42 43
Momentum, angular 11 61 64 88 93 95 101 105 115 125 130 135
Momentum, linear 10 64 93 101 105 112 120 135
Monodromy matrix 75
Multipliers 73 75 78 81 84 85 90 97 99 100 102 107 114 125
n-body problem 1 9—11 63—64 100—101 112 131
Noether's theorem 61—63
One-parameter sub-group 58
Orbital stability 79
Poincare 2 77 87 90
Poisson bracket 62
Reduced space 65 88 95 102 107 115—116 125 135—136
Reduction 3 65—70 101—102
Relative equilibrium 41—42 86 100 106 108 132—133
Relative equilibrium, characteristic polynomal 42
Relative equilibrium, characteristic polynomial 48 49
Relative equilibrium, Euler — Moulton 43—45
Relative equilibrium, exponets 41
Relative equilibrium, Lagrangian 42—43
Relative periodic solution 58
Remainder function 21
Restricted N + 1-body problem 91 117
Restricted problem 12—15 51 86 90—103 110 126
Reversible 51 70 86
Roberts, Gareth 86
Symmetry of an equation 54
Symmetry, group 55 64
Symplectic coordinates 20—32
Symplectic flow 22
Symplectic group 20
Symplectic matrix 20 37
Symplectic scaling 3 36—37
Syzygy 14 52
Variational equation 21 89 114
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