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Reithmeier E. — Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos
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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 171

Добавлена в каталог: 21.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$T^{2}$-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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