|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Brauer F., Nohel J.A. — The qualitative theory of ordinary differential equations |
|
|
|
| Предметный указатель |
Matrix differential equation 105 106 300
Matrix function 36
Matrix function, continuous 36
Matrix function, differentiable 36
Matrix function, integrable 36
Matrix norm 35 36 56
Matrix polynomial 80
Matrix, almost periodic 159
Matrix, block diagonal 76 278 279
Matrix, constant 50 55 72 99
Matrix, constant diagonal 62
Matrix, constant nonsingular 89
Matrix, continuous 40
Matrix, diagonal 58 75 77 265 275 276
Matrix, elementary operations of 34
Matrix, inverse 35
Matrix, Jordan canonical 282 283
Matrix, nilpotent 80 287
Matrix, nonsingular 35 50 52 56 77 90 97 274 275
Matrix, nonsingular constant 49 50 62 73 96
Matrix, periodic 96 159 184—186
Matrix, positive definite 271 298
Matrix, rank of 68
Matrix, real nonsingular 97
Matrix, real symmetric 268
Matrix, similar 74—76 89
Matrix, similarity of 73—80
Matrix, stable 265 267 299 300
Matrix, symmetric 264 298
Matrix, symmetric, positive definite 264—267 299—301
Matrix, triangular 62
Mean value theorem 122 160 173 184 240
Mechanical system 106 205
Minimal polynomial 153
Minimum potential energy 188
Model 9
Momentum 2
Motion 3—6 22 84 147
Multiplicities 185
Multipliers 98 99—102 159 185 186
Natural frequencies 107
Negative semiorbit 192
Newton 1
Newton's first law 1
Newton's second law 1—3 9
Newtonian model 1 2
Nilpotent 79
Nilpotent matrix 80 287
Nilpotent transformation 65 280
Nilpotent transformation of index 280 281
Node 103
Nonautonomous system 147 150 193 228—236
Nonhomogeneous system See Linear systems
Nonlinear systems 144 159 164 200
Nonlinear systems, control of 263
Nonlinear term 161 163 169 172
Nonsingular matrix See Matrix
Norm 26 38
Norm of vector 17
Norm, properties of 38
Null space 277
Optimal control 237
Orbit 85 87 90—93 95 164 192 193 197 200 211—213 259 260
Orbit of solution 85
Orbital stability 186
Oscillations, forced 260
Oscillations, self-excited 250—261
Oscillator, damped linearized 194
Oscillator, linear damped 251
Oscillator, linear undamped 250
Oscillator, nonlinear undamped 250
Oscillator, undamped 238—244
Osgood condition 140
Osgood uniqueness theorem 140
Particle 1 2
Particular solution 55
Particular solution of nonhomogeneous system 72
Path 85
Pendulum 6 7 244—250
Pendulum equation 84
Pendulum equation, nonlinear 89
Pendulum equation, simple 89 200
Pendulum equation, simple undamped 86
Pendulum, damped 191 237
Pendulum, damped simple 163 164
Pendulum, simple 22 23 201
Pendulum, simple undamped 145 146 177 197 244—246
Pendulum, undamped 237
Period 238 239 244 245 250
Periodic matrix See Matrix
Periodic solution 102 180 193 222 238 239 245 248 251 256 260
Periodic solution of autonomous systems, stability of 186
Periodic solution of Lienard equation 250—261
Periodic solution of nonlinear periodic systems, Periodic solution, stability of 144
Periodic solution, asymptotically stable 184 185
Periodic solution, stability 183—186
Perron 161
Perturbation 89 169 232
Perturbation term 89 95 164 171
Perturbed equation, asymptotic stability of 170
Perturbed system 89 90 161 164 169 170
Phase 85
Phase plane 86 154 164 171 190 222 239 253 254 259
Phase portrait 87—91 93—95 103 164 171 199 200 245 248—250
Phase portrait of linear two-dimensional systems 88
Phase space 83—95 145 149 160 192 196
Physical approximations 22 23
Physical assumptions 3
Physical phenomena 3
Physical problems 6
Physical system 1 5 22 251 261
Poincare method 261
Poincare phase plane 85
Poincare — Bendixson theory 237
Poincare, H. 143 161
Polar coordinate 94
Polar form 94
Positive limit set 211—214 258
Positive semiorbit 192 210 211 213 258
potential energy 188—191 194 197 200
Potential function 188
Principal minors 265 298
Proof by induction 113 115 134 276
Proper node 91
Quadratic form 264
Quadratic form, positive definite 264
Qualitative phenomenon 144
Qualitative properties 143
RANGE 279
Range of linear transformation 277
Rayleigh equation 259
Reactor dynamics 223 227
Region 10 21 24 28. region
Regulator problem 237 261—267 270 296
Regulator system, absolute stability of 267—273
Resistance 10
Rest position 187
Restoring force, of a spring 197
Routh — Hurwitz criterion 154 155
Row vectors 34
Saddle point 92 95 103 171 200 219
Saddle point of linear unperturbed system 178
| Saddle point of perturbed system 171
Scalar differential equation 39 47—49 71 95 99 100 103 108 122 151—154 171 205 233
Scalar differential equation, asymptotically equivalent 179
Scalar differential equation, higher-order 30
Scalar differential equation, linear 51
Scalar differential equation, of order n 54 122
Scalar differential equation, of second order 54 71
Scalar linear equation 51
Schwarz inequality 18 19
Semiorbit 211 212
Separation of variables 11 12 149 155 169
Separatrix 250
Sequence, of matrices 55
Series of matrices 55
Series of matrices, convergence of 55
Series of matrices, sum of 55
Servomechanism 262
Similar matrices See Matrix
Similarity invariants 74
Singularly perturbed system 237
Solution 9 11 30
Solution curve 11
Solution matrix 45 46 48 49 57 96
Solution space, basis for 44
Solution, asymptotically stable 148 149 151 169 187
Solution, bounded 154 158 181 182 196 202 212 213 215 223 225—227 230 235
Solution, global behavior of 228
Solution, globally asymptotically stable 149
Solution, instability of 187
Solution, linearly independent See Linearly independent solutions
Solution, periodic See Periodic solutions
Solution, stability of 187
Solution, stable 148 149 151
Solution, structure of 40
Solution, unbounded 251
Solution, unique 30 37 39 40 48 51 132 135
Solution, unstable 151
Solution, zero See Zero solution
span 280
Spiral point 94 103 164 219
Spring 7 106 107
Spring, constants of 7 106 107
Spring, hard 244
Spring, linear 3 244
Spring, nonlinear 5 201 251
Spring, soft 244
Stability 144—151 157 159—161 184 196 197 201 202 204 205 208—215 228 230
Stability criterion 155 230
Stability matrix 261 263
Stability theory, of periodic solutions 169
Stability, absolute 267—273
Stability, asymptotic See Asymptotic stability
Stability, conditional See Conditional stability
Stability, of almost linear systems 143—151 160—171
Stability, of linear systems 143—159
Stability, of periodic solutions 183—186
Stability, of solutions 148
Stability, of zero solution 150 152 165 192
Stability, uniform 147
Stability, with global properties 152
Stable equilibrium 188
Stable equilibrium point 188
Steady state See Equilibrium
Sturm — Liouville boundary value problem 141
subspace 40 61 64—66 68 76 274 277 280 281
Subspace, direct sum of 279 282
Subspace, disjoint 277
Subspace, index of 277
Subspace, one-dimensional 63
Subspace, spanned 68
Subspace, spanned by eigenvectors 61
Successive approximations 111 113 114 117—124 127 134 139 141 174 182
Successive approximations, convergence of 127 138
Sylvesteres theorem 265 269 298
Symmetric matrix See Matrix
Systems absolutely stable 262
Systems absolutely stable, asymptotically autonomous 234—236
Systems absolutely stable, asymptotically equivalent 181
Systems absolutely stable, first order 10—15
Systems absolutely stable, linear algebraic 64
Systems absolutely stable, of algebraic equations 48 68
Systems absolutely stable, of differential equations 128
Systems absolutely stable, of first-order equations 197
Systems absolutely stable, of linear algebraic equations 35
Systems absolutely stable, of linear equations 64
Systems absolutely stable, of two differential equations 9
Systems absolutely stable, of two second-order equations 14
Tangent vector 11
Taylor's theorem 245
Total energy 188 189 191 194 195 197 198 200 201 209
Trajectory 85
Triangular matrix See Matrix
Two-dimensional systems 83—95 271
Type numbers 159
Uncontrolled system 272
Uniform convergence 116 134
Unique solution 30 37 39 40 48 51 132 135
Uniqueness 24—30 125—127 130
Uniqueness of initial value problem 192
Uniqueness of solutions 27 28 30 52 108 119 124—127 137 145 148 175 176 192 206
Uniqueness problem 23
Uniqueness theorem 126
Uniqueness, periodic 256 257
Unperturbed equation 170
Unperturbed system 171 172 232
Unperturbed system, asymptotically stable 171
Unperturbed system, unstable 171
van der Pol equation 222 237 251 252
Van der Pol equation, unstable 251
Variation of constants formula 53 71 72 82 102 162 165 170 181 182
Vector 37 124
Vector algebra 17
Vector differential equation 15
Vector field 84
Vector function 21 26 36 37
Vector function, continuous 20
Vector function, differentiable 20
Vector function, integrable 20
Vector norm 36
Vector space 40 43 45
Vector space, abstract 40
Vector space, axioms for 40
Vector space, basis for 42 43
Vector space, dimension of 41—44
Vector space, finite-dimensional 42
Vector space, of continuous functions 40—42
Vector, constant 49
Vector, linearly independent 35
Vector, sum of two 17
Vector, zero 17
Vector-matrix notation 15—22
Velocity vector 84
Voltage drop 10
Voltage, impressed 10
wronskian 48 49
Zero solution, asymptotically stable 154 158 161 169 185 195 201 202 204 214 215 220 223 231 232 233
Zero solution, globally asymptotically stable 156—158 161 223—225 227 228 235 236 269 271
Zero solution, instability of 192
Zero solution, stability of 150 152 165 192
Zero solution, stability properties of 160
Zero solution, stable 153 154 157 159 169 195 200 202 207 229 230
Zero solution, unstable 154 159 172 195 208 222
Zero vector 17
|
|
|
| Реклама |
|
|
|
|
|
О проекте