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

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

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

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Planet oblate      219—221 224 225
Planet perturbed      183
Planet perturbing      183
Planetary perturbation      186
Planetary system      183
Poincare — Lyapunov domain, neighborhood      5—7 70 71 73 74 77
Poincare — Lyapunov theorem      5 7 70 73
Poincare, H.      5 10 124 143 184—186
Poisson bracket      134 136 234
Poisson commuting      153
Polar axis      219
Polar coordinates      69 73 78 81 100 157 208 212 217 226
Polar orbit      223
Population density      19 67
Population growth      19
POSITION      132
Position equilibrium      144
Position general      149 150 155 156 160 161 166 169 172—174
Position line of apsides      101
Position variable      167 181
Position vector      218
Pull-back      128 233
Quasilinear      19 24
Resonance      34 83 85 101 102 105 106 108 109 120—123 137 143—146 149 163 164 166 169 172 175
Resonance 1:1-      137 154 156
Resonance 1:1:1-      164
Resonance 1:1:3-      164
Resonance 1:2-      151 153 154 169 173
Resonance 1:2:1-      164 166—168 171
Resonance 1:2:2-      168—170
Resonance 1:2:3-      163 170 171 204 206
Resonance 1:2:4-      172 173
Resonance 1:2:5-      163 174
Resonance 1:3-      156 158
Resonance 1:3:3-      164
Resonance 1:3:5-      164
Resonance 1:—1-      137
Resonance 2:2-      154
Resonance 4:1-      161
Resonance 4:3-      161
Resonance 9:2-      161
Resonance angle      120
Resonance condition      106 108
Resonance coordinates      149
Resonance domain      106 107 120 122 123 151 198 223 224
Resonance first order      141 163 164 172 173
Resonance genuine      139 141 163 164 168 173
Resonance higher order      159 160 163 223
Resonance k:l-      149 154
Resonance locking      106 107 118 122 123
Resonance manifold      102—104 106 107 112 114 117 121 123 161
Resonance matrix      149
Resonance Mth order      141
Resonance non-      144
Resonance order of      163
Resonance passage through      59 83 105 108 109 114 117 118 122 123
Resonance region      109 198
Resonance relation      141
Resonance second order      141 156 163 164
Resonance systems in      34
Resonance term      141 142
Resonance variable      106
Resonance zone      145 151 160
Resonant      142 198
Resonant limit      199
Routh — Hurwitz criteria      210
Sanchez — Palencia, E.      34 70 71 76
Satellite      181
Satellite mechanics      219
Satellite orbit      220
Section conic      Conic section
Section Poincare      153 159
Secular      182 184
Secular equation      183—186
Secular perturbation      33 183 186
Secular variation      183
Secularity condition      186 189 191 192
Self-interaction      142
Series      9 15 182 183 220
Series (co)sine      183
Series asymptotic      13 15 186
Series convergent      9 56 185 219
Series divergent      10 6
Series expansion      185 186 226
Series formal      197
Series Fourier-      105 184
Series infinite      119
Series orthonormal functions      9
Slowly decreasing (with time)      100
Slowly varying angle      146
Slowly varying coefficients      83
Slowly varying frequency      83 84 89 93 129
Slowly varying length      60
Slowly varying mass      33
Slowly varying system      83
Slowly varying terms      59
Slowly varying with time      60 187 227
Species      19 67—69 74
Sphere      146 149 162 231 232
Stability      5 122 146 162 163 174
Stability characteristics      5 79 165
Stability criteria      210
Stability linear      165
Stability Lyapunov      214
Stability of airplanes      189
Stability type      152
Stable      4 5 146 163 169 171 201
Stable and unstable manifold      202

Stable asymptotically      5 7 34 73 75 80 210
Stable attractor      42
Stable critical point      34 71 75
Stable equilibrium      143—146 163
Stable limit-cycle      25
Stable Lyapunov      4 5
Stable manifold      103 118 208
Stable orbit      169 171—174
Stable periodic solution      25 66 153 161 166 172
Stable solution      123 171
Stable stationary point      78
Standard form      3 18—21 24—27 29 31 33 36 42 59 60 61 65 83 87 125 137 156 157 183—185 189 190 221 227
Stationary point      78 80 132 150 151 5 156
Stationary solution      80 89 154
Superposition      181
Symbol Landau      11
Symbol O(.)      36 40
Symmetric 1:1-resonance      154
Symmetric anti      233 234
Symmetric axi      219
Symmetric discrete      168
Symmetry      167 169
Symmetry approximate      170
Symmetry assumption      154 164 167 171
Symmetry axi      223
Symmetry axial      220
Symmetry discrete      167 171—175
Symmetry mirror      154 67 171
Symplectic approximately      133
Symplectic coordinates      136 154
Symplectic coordinates change of      145
Symplectic diffeomorphism      233—235
Symplectic form      132 233 235
Symplectic manifestly      132
Symplectic manifold      233
Tangent bundle      232
Tangent plane      232
Tangent space      152 232
Tangent vector      232
Taylor-expansion      15 102 137 234
Time-axis      74
Time-independent      125 127 184
Time-interval      213
Time-like variable      12 60 94 98 119 189 218 221 223 225 227 229
Time-scale      13 17 28 29 31 34 51 62 68 70 71 79 81 83 99 101 104 105 111 114 144 161 208 213 221 223
Time-scale $1/\delta(\epsilon)$       13 104
Time-scale $1/\delta_{1}(\epsilon)$       23
Time-scale $1/\epsilon$       21 22 25 28 29 31 32 34 37—48 50 51 55 57 59 61 62 64 67 70 79 81 92—94 96 97 99—101 118 154 163 187 191—193 208 222 223 226—229
Time-scale $1/\epsilon^2$       29 62—64 66 79 80 82 161
Time-scale $1/\epsilon^{1/2}$       105 110
Time-scale $[1, \infty)$       67
Time-scale $\epsilon^{-m}$       144
Time-scale $\epsilon^{-\frac{k+l}{2}}$       162
Time-scale 1      16 17 22 73 99 229
Time-scale exponential      144
Time-scale extension      117
Time-scale multiple      34 118
Time-scale natural      103 105 114 168
Time-varying      229
Torus      84 144 146 149 154 162 232 234
Torus invariant      143 144 149 162
transform      4 14 15 42 62 73 84 85 90 93 98 108 124 156 184 210 212 218 220 221 225 227 235
Transform Lie      132
Transformation      25 29 52 124 134 154 157 184 189 204 209 221 224 228
Transformation action-angle      137 138
Transformation averaging      88 91 95 102 120 197 198 199
Transformation canonical      221
Transformation coordinate      124 127 196
Transformation linear      26 124 166 169 210 212
Transformation near-identity      125 128 134 210
Transformation normalizing      133 138
Transformation phase-apmplitude      21 24 25 27 29 80 84 119 121 186
Transformation symplectic      133 152 166 190
Transformation time-scale      83 94
Transformation variation of constants      18—21 26 27 184 186
Translation-number      55
Transversal      102 105 148 159
Transversal coordinate      105
Transversal locally      146
Transversality condition      202
Triangle inequality      41 46 47 63 72 77 193
Uniqueness      118 141
Uniqueness existence and      1—3 6 15 22
Unperturbed equation      18 73 74 201 212
Unperturbed flow      76
Unperturbed problem      15 16 18—20 138 152 182 184 185 195 196 217
Unperturbed system      201
Unstable      26 73 80 169 171 172 201
Unstable critical point      25
Unstable manifold      118 202
Unstable normal mode      166 169 171 172
Unstable periodic solution      161 166
Van der Aa, E. vi      166 169—173
Van der Pol, B.      184 186
Van der Pol, B. equation      24 25 51 66 69 73 78 79 186
Van der Pol, B. modified      65
van der Sluis, A.      76
Vectorfield almost-periodic      54 56 58 59 187
Vectorfield averaged      24 70 113 213
Vectorfield Hamiltonian      136
Vectorfield inner      102 105
Vectorfield inner-outer      104 105
Vectorfield KBM      36 39—41 43 44 46 48 55 70 71 75
Vectorfield monotone      117
Vectorfield periodic      56
Vectorfield v      5 10 15 24 34 35 44 48 50 52 55 59 70 74 75 78 80 90 98 104 112 115 120 124—129 132 136 137 187 196 206 212 232—234
Weinstein, A.      144 145 172
Zone, resonance      145 160

1 2 3

О проекте