Sanders J.A., Verhulst F. — Averaging methods in nonlinear dynamical systems :: Электронная библиотека попечительского совета мехмата МГУ

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Sanders J.A., Verhulst F. — Averaging methods in nonlinear dynamical systems

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Название: Averaging methods in nonlinear dynamical systems

Авторы: Sanders J.A., Verhulst F.

Аннотация:

In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field.

Язык:

Рубрика: Физика/Динамические системы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 247

Добавлена в каталог: 28.09.2005

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Предметный указатель

action      144 146 147 150 162 165 204 234
Action level      206
Action of a transformation      166 212
Action simplex      165 167—171 173 174
Action variables      145 162
Action-angle coordinates      149 204
Action-angle variables      137 141 149 151 164 166 234
Adiabatic invariant      94 101
Aerodynamic      224 226
Almost-periodic      54—57
Almost-periodic differential equation      55
Almost-periodic equation      34
Almost-periodic function      54—57
Almost-periodic solution      54
Almost-periodic vectorfield      54 56 58 59 187
Angle action      Action-angle
Angle azimuthal      219 223
Angle combination      145 146 149 165 166 168 170 172 173 204
Angle resonant      120
Annihilator, annihilation vector      138 139 163 164 173
Approximate      10 12 26 52 64 67 75—78 89 96 213 229
Approximate character      89
Approximate integral      108 162 165
Approximate solution      28 29 182 186 207 228
Approximate symmetry      170
Approximately      42 127
Approximately symplectic      133
Approximation      9 10 13 17 29 31 34 43 59 62 64 67 68 70 77—82 85 98 108 110 116 117 161 163 183 186 189 190 202 208 213 222 223 226 228 229
Approximation accuracy of the      17
Approximation asymptotic      9 10 13—17 24 26 28—32 34 59 62 71 82 87 89 91 144 163 207 214
Approximation crude      30 31
Approximation first      27
Approximation first order      35 43 51 63 97 101 183 192 212 222
Approximation formal      17 89 107
Approximation global      106
Approximation higher order      43 81 82 94 101 155 191 192 223 224
Approximation linear      71 73 82
Approximation numerical      76 207
Approximation order of      52 221
Approximation process      1 10 77
Approximation result      64
Approximation scheme      77
Approximation second order      35 43 45 46 49 50 122
Approximation technique      9
Approximation theorem      56
Approximation theory      33
Approximation uniformly valid      77 81
Arnol'd, V.I. vi      89 106 125 144
Arnol'd, V.I. vi -diffusion      144 163
asymmetric      169
Asymptotic      118 146 174
Asymptotic accuracy      154
Asymptotic analysis v, vi      10 105 109 163 228
Asymptotic approximation      9 10 13—17 24 26 28—31 34 59 62 71 82 87 89 91 144 163 207 214
Asymptotic character      107
Asymptotic computation      207 215
Asymptotic construction      136
Asymptotic estimate      3 52 83 118 143 160—162
Asymptotic expansion      13 15 77 138
Asymptotic result      21 208
Asymptotic series      13 15 186
Asymptotic solution      105
Asymptotic theory      v
Asymptotic validity      103 187 189
Asymptotically      72 105 215
Asymptotically equivalent      192
Asymptotically stable      5 7 34 71 73 75 80 210
Asymptotics      9 118 122 143 146 160
Atmosphere      224 226
Atmospheric drag      224
Attract      67 69—71 73 75 78 122 123 208 213
Attraction      1 4 5 7 34 62 67 68 70 73 76 79—82 190 208
Attraction domain of      34 67 68 71 73 74 77 213
Average      21 24 29 30 34—36 39 41 46 48—50 52 56 59 60 64 68 85 88 90 95 97 98 102 113 114 117 121 125 127 130 136 161 183 186 192 198 212 222
Average general      45
Average generalized      93
Average local      34 35
Averaged      35 104 224
Averaged equation      21 24 27 55 64 66 70 71 75 78 80 82 89 103 104 106 115 119 124 167 199 212 213 221 223 225—228
Averaged second order      51 78 82
Averaged system      69 78 213 223
Averaged vectorfield      24 113 213
Averaging crude      29 30
Averaging elementary      23
Averaging first order      21 23 52 184 221 222 225
Averaging general v      34 39 41 43 46 48 50 52 54 55 65 187
Averaging higher order      168
Averaging method      105 182 184 186 187 190 191 207 208 228
Averaging periodic      34 39
Averaging process      73 79 103
Averaging second order      48 96
Averaging technique      101
Averaging theorem      23 39 41 70 72 92 228
Averaging theory (of)      21 33—35 54 59 83 181 186 187 213 216
Averaging transformation      88 102 120 197—199
Averaging v      21 26 27 29 31 33 34 42 49 51 54 55 61 69—71 73 80 81 83 88 94 104—108 122 128 182—184 187 189 190 192 195 213 222
Averaging validity of      34
Bessel function      219
Bifurcation      153 155 157 167 172
Bifurcation behavior      207
Bifurcation curve      158
Bifurcation diagram      146
Bifurcation equation      155 157
Bifurcation global      155 169 174
Bifurcation Hopf      207
Bifurcation set      145 151 156 157 169
Bifurcation value      153 159
Birkhoff, G.D.      124
body      226
Body one      181 183
Body primary      224
Body three      216
Body two      33 100 181 182 219 224 226 228 229
Bogoliubov, N.N. v      23 34 36 52 187 189
Boundary      104 114 145 148 161
Boundary condition      9
Boundary layer      102—104 161
Bracket Poisson      134 136
Bundle circle      158
Bundle cotangent      132 134 136 232—234
Bundle normal      152
Bundle tangent      232
Bundle vector      232
Canonical perturbation      185
Canonical transformation      221
Canonical variables      145 204
Cardioid      157
Celestial mechanics      60 97 100 184—187 216 217
Chow, S.N.      119
Circle(s)      78 84 147 148 154 232
Circle(s) bundle      158
Circle(s) invariant      149
Circle(s) linked      149
Circle(s) pencil of      158
Clairaut, A.      182 184
Commutator      126
Commute      136 138 153
Composite expansion      104 105
Conic section      182 218
contracting      77
Contracting exponentially      72 75
Contracting map      75 76
Contraction      1 3 76 82 187
Contraction constant, factor      77 82
Coordinate      66 94 105 124 132 137 146 204 212 234
Coordinate action-angle      149 204
Coordinate change of      145
Coordinate complex      137 141 149 167
Coordinate elliptical      183
Coordinate local      126 128 132 134 137 231 233 234

Coordinate mixed      132
Coordinate phase-amplitude      60
Coordinate polar      69 73 78 81 100 157 208 212 217 226
Coordinate real      151 158
Coordinate relative      217
Coordinate resonance      149
Coordinate spherical      218 219
Coordinate symplectic      136 154
Coordinate system      137 216 217 228
Coordinate transformation      84 124 127 128 196
Coordinate transversal      105
Cotangent bundle      132 134 136 232—234
Cramer's rule      139
Critical inclination      223 224
Critical orbit      152
Critical point      25 34 69—71 73 75 80 118 132 136 146 162 165—167 169 171 172 234
Cushman, R. vi      137 165 169
Cusp      157
Damping      61 80—82 86
Damping coefficient      42
Damping increasing      42 48
Damping linear      30 61 68 81 82
Damping nonlinear      81
de Laplace S.P.      33 182 184
Decomposition      183
Degree      219
Degree homogeneous      137 138
Degree of freedom      162 174 234
Degree of freedom first      148 171
Degree of freedom n      132 133 143—145 153 162
Degree of freedom one      27 146 163 172 174
Degree of freedom second      147 148 171 173
Degree of freedom third      171 173
Degree of freedom three v      141 144 162 163 165 166 217
Degree of freedom two v      137 141 142 144 146 147 149 151 153 154 156 161—163 172 174 223
Degree polynomial      133 157
Degree third      167
Delaunay, C.      124
Dense, relatively      55
Detuned      166
Detuning      145 149 153 160 169 204
Diffusion      Arnol'd diffusion
Dissipative      190
Dissipative force      224
Divisor, small      138
Domain      5 10 56 71 160 161
Domain bounded      52
Domain excluded      101
Domain inner      104 105 112 118
Domain interior      76
Domain of attraction      34 67 68 71 73 74 77 981 213
Domain of definition      50 231
Domain of validity      10 11
Domain outer      114 115 161 162
Domain resonance      106 107 120 122 123 198 223 224
Domain triangular      165
Duffing's equation      80 ; see also “Perturbation”
Duistermaat, J.J. vi      166 167
Dulac      124
Dynamical system v, vi      146 185 216 231
Dynamical theory      181
Dynamical variable      218
Eccentric anomaly      101 228
Eccentric rotor      121
Eccentricity      101 182 183 218 228
Eckhaus, W. vi      10 14 34 35 70 71 76 117
Egenfrequency      122 143 144
Eigenspace      209 210
Eigenvalue      5 6 20 67 70 73 74 80 122 137 155 165 206 208—211
Eigenvalue conjugate      165 210
Eigenvalue imaginary      165
Eigenvalue real      165
Eigenvalue zero      127 165
Einstein, A.      84 89 93
Elastic support      121
Elliptic      152 153 159 160 162 165
Elliptic critical point      162
Elliptic fixed point      153
Elliptic function      18 119 120 195 196
Elliptic integral      119 120 226
Elliptic orbit      101 153 155 162 163 228
Elliptic solution      120 153
Elliptical coordinates      183
Energy      94 144—147 165 166 173 183 217 220 228
Energy exchange      161
Energy integral      119 221
Energy level      143 145 152
Energy manifold      144 146 147
Energy plane      169
Energy surface      149
Equilibrium      136 137 143 145 206
Equilibrium point      143 144 163 234
Equilibrium position      144
Equilibrium solution      26 122
Equilibrium stable      143—146 163
Euler, L.      9 10 14 124
EXIST      3—6 11 12 15 17 22 35 36 49 55 76 93 108 123 127 132 139 140 143—145 154 162 163 165 167 169 171 172 185 187 201 232 234
Existence      3 64 77 91 99
Existence almost-periodic solution      54
Existence and uniqueness      2 22
Existence integral      167 169 220
Existence orbit      223 224
Existence property      72
Existence solution      3 6 22 146 151
Existence theorem      1—3 6 15 64
Existence tori      144 162
expansion      11 13—15 74 88 106 109 114 169 181—183 189—192
Expansion asymptotic      15 77 138
Expansion binomial      226
Expansion composite      104 105
Expansion Fourier-      58 59 106 120
Expansion inner      102—104 109
Expansion inner-outer      104 105
Expansion local      103
Expansion method      105
Expansion multiple time scales      189 190
Expansion naive      81
Expansion outer      103 104 109
Expansion procedure      104
Expansion series      185 186 226
Expansion Taylor-      15 102 137 234
Flip-orbit      153
Flipping through      159
Fly-wheel      86 121
Foliation      149 154
Fourier expansion      58 59 106 120
Fourier series      105 184
frequency      60 85 86 94 102 145 173
Frequency constant      136
Frequency eigen      122 143 144
Frequency modulation      25
Frequency multi      88 98
Frequency shift      215
Frequency slowly varying      83 84 89 93 129
Frequency vector      137
Fresnel-integral      109
Generating function v      132 133
Genuine      Resonance genuine
Geometric v      146
Geometric v interpretation      216 217
Geometric v picture      146 149
Geometric v variable      218
Geometry vi classical      232
global      42 122 143 163
Global analysis      231
Global approximation      106
Global bifurcation      155 169 170
Gravitation      181
Gravitational constant      60 86 101 217 218 226 229
Gravitational field      218

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