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| Reithmeier E. — Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos |
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Название: Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos
Автор: Reithmeier E.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1991
Количество страниц: 171
Добавлена в каталог: 21.07.2008
Операции: Положить на полку |
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| Предметный указатель |
 -HOPF bifurcation 149
(m : n)-cycle 132
Algebraic constraints 12 14 16 20 79
Algebraic equation, nonlinear 3 121
Algorithm, numerical 5
Amann 6
Amplifier 3
Amplitude jumps 84
Analytic 39
Analytical espression 136
Analyticity of the dynamical system 17 18
Angles of rotation 11
Approximation theory 3
Areas of convergence 32
Arnold 20 33 42 64
Asymptotic stability 8 85 140
Attraction, domains of 66
Autonomous system 6 28 49 132
Backlash 110 114
Bajaj 8
Bearing 71
Behavior, bifurcation 7
Behavior, dynamical 9
Behavior, global 19
Belt 3
BENDIXON 7
Berger 6
Bifurcation 3 7 47 53 66
Bifurcation parameter 82
Bifurcation point 82
Bifurcation tree 147
Birkhoff 6
Block diagonal matrix 14
Block GAUSS step 133
Body fixed frame 68
BOTTKOL 7
Boundary condition 49
Boundary value problem 6 46 67 79
Boundary value problem, standard 53
Boundary value problem, two point 47
Bulirsch 7 53 55
Cardanian angles 11
Center 11
Center line 75
Center manifold theorem 33
Center of mass 12 14
Chain 3
Chain rule 23 50
Chuster point 86
Classification of singularities 33
Codimension 36 39 40 42 43 86
Complementary set 141
Complex eigenvalue 143
Concentric circle 144
Cone angle 10
Cone surface 12
Cone, double 10 75
Configuration coordinates 17 49
Configuration space 5 36 64 114
Configuration, unbounded 17
Connected component 28 58 76 106 123
Conservative system 33
Constraint, algebraic 72
Contact ellipsoid 69
Contact forces 12 68 97
Contact, permanent 14
Contact, point of 12 117
Control function 9
Control scheme 12
Control space 11
Control vector 18
Controlable 12 20
Convergence of a series 20
Coordinate mapping 70
Coordinates, surface oriented 13 81
Corank 35 42
Cost function 76
Coy 114
Criterion 76
Critical point 6
Critical variable 38
Damper 47
Damping element 3 127
DE PATER 8 75
Decomposition of the JACOBIan 133
Decomposition, triangular 135
Degenerated 33
Degenerated direction 35 36 38
Degenerated fixed point 35
Degree of freedom 4 5 14
Determinant 143 147
Deuflhard 7 52
Diagonal form 24 77
Diekhoff 55
Diffeomorph 27
Diffeomorph transformation 32
Differentiability, partial 9
Differentiable 9
Differential topology 6
Differential-algebraic-equations 12 71
Discontinuities 8 110
Discrete steps 56
Disjunct open set 112
Dissipative system 20
Disturbance of an initial condition 9
Domains of attraction 66 85
Double pendulum 36 47 54 107
Drag of rolling friction 68
Dry friction 3 114 136
Duffing oscillator 7 28
Duistermaat 7 47
Dulac 20
Eigenmode 55
Eigenmode, periodic 73 105
Eigenspace 34
Eigenvalues, linear combination of 33
Eigenvalues, multiple 24 25 26 30
Eigenvalues, pure imaginary 33
Eigenvalues, zero 33
Eigenvectors 24 30 73
Ekeland 6
Elementary functions 20
Embedded 36
Energy parameter 55—65
Energy range 108
Energy value 55—65
Equilibrium of the system 27
Equilibrium, points of 19 45 54
Equivalence class 39
Ergodic 149
Excitation, amplitude of 3
Excitation, harmonic 5
Excitation, outside 5
Excited system 20
Excited, externally 4 110
Excited, harmonically 28
Excited, internally 4
Existence of periodic solutions 6
Fibering, trivial 113
First order system 28
Fixed end point 53
Fixed point 3 6
Floquet exponent 79
Flow on a manifold 34
Fourier coefficient 17
Fourier expansion 17
Frame body fixed 11
Frame, inertial 11
Friction coefficient 69
Friction force 114
| FUEHRER 12
Fuller 6
Gauge 11
GAUSS — NEWTON-technique 7 52
Gear box 3
Gear multistage 3
Gear, non-loaded 3
Generalized acceleration 18
Generalized coordinates 46 49
Geodesics, closed 6
Germ of a function 39
Gordon 6
Gradient 39 46
Griepentrog 12
GROBMANN 33 44
Hamilton 4 33
Hamiltonian function 4 33 51 53
Hamiltonian system 45 67
Harris 6
Hartman 33 44
HEIMANN 8
HERMITE-interpolation 92
Hesse-Matrix 7 35 38 80
HOLODNIOK 7
Homeomorph 33 142
Homoclinic orbit 55 56 60 63
Homogenous system 13
Homological equation 21 23
Homotopic deformation 58 59
Homotopy parameter 67
Hopf 3 6 66
Hopf bifurcation 93 94 145
Hopf theorem 95
Hsu 7
Image 36
Impact model 111
Impact parameter 145
Implicit function theorem 19 51 101
Impulse coordinates 46
INDEX function 86
Index, topological 6
Indicator function 122 125
Inertial frame 11
Initial function 55
Initial value problem 9
Injective 86
INTEGER 24 58
Integral criterion 76
Integral, first 7
Intersecting point 87
Invariance of translation 132
Irregular behavior 3
Isolated point 49
Isomorph 113
Isomorphic, locally 9
Jacobian matrix 33 51 73 138
JASCHINSKI 68
JOCHIM 68
Jordan curve 7
Jordan normal form 23 25
JOURDAIN, principle of 14
K-type of periodic solutions 58
KALKER 68
KALKER coefficients 69
KARAGIANNIS 8 110
Kernel 36
Kinks 148
Klingenberg 64
KUBICEK 7
KUECUEKAY 114
LAGRANCE-multiplier 13
Laser optics 3
Lateral deviation 75 83
Lewis 6
Liapunov 8
LIAPUNOV stable 85 86
Libration 55 83
Limit cycle 3 66 140
Limit function 5 86
Limit, stable 105
Linear independent 107
Linear mapping 36
Linear system 20
Linearized Equation 26
Linearized system 30 66
Linearized vector field 32
Lipschitz continuous 100 111
Local transformation 103
Locally isolated 76
Locally separated 50
LOETSTEDT 12
lu 42
MAERZ 12
Magnus 3
Manifold 7 32 86
Manifold, center 34
Manifold, differentiable 9 46
Manifold, invariant 34
Manifold, stable 34
Map, linear 19
Markus 6
Mass matrix 6
Mean value theorem 49
Measure of stability 77
MEIJAARD 8 75
Metric 64
Meyer 7
MICKENS 18
Microphon 3
MIL'SHTEIN 7
Minimax problem 6
Minimize 78
Modulus 143
Moments of inertia 11
Monodromy matrix 66 77 94 99 106
Monodromy operator 91
Monomial 21
Monomial non-resonant 25
Monotonously 86
Moser 6 8 33 45
Motion, equation of 11 12 17 48
Mounted, elastically 71
Mueller 7
Multibody system 14
Multiple shooting 5 55 93 133
Multiple staged rattling model 114
Necessary condition 5
Necessary condition for bifurcation 100
Neighborhood 12
Neighborhood, open 19
Non-autonomous 14 140
Non-holonomous 14
Non-resonant 20 31
Non-singular matrix 30
Normal force 69 114
Normal form 4 20 45
Numerical computation 54—64 132
Open neighborhood 44
Operator equation 24
Operator, linear 24
Optimization strategy 9
Optimization technique 7
Optimization, standard problem of 79
Orbit, homoclinic 55
Parameter space 11 36 141
Parameter values 11
Particular solution 123
Partition of statespace 112 128
Passive force 117
Period doubling 95 142
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