kinetic, 176
near-elastic, 175
pendulum, 101, 368
printers, 377
state, 367
systems, 366
Imperfection, 296, 378, 438
Impulse response function, 5
Inclusion theorem, 73
Incommensurate frequencies, 293, 328
Information dimension, 339
Instationary force, 43
Instationary system, 44
Integral curve. See Orbits
Interaction, nonlinear, 209
Interface, to ODE-solver, 452
Intermittency, 345, 347, 349
route to chaos, 345
type-I, 346, 349
Internal
detuning, 218
resonance. See Resonance
Internet resources, 454
Invariant
manifold, 286, 351
mode, 308
Inverse iteration, 51
Inverse tangent bifurcations, 346
Isola, 307, 310
J
Jacobian, 108
eigenvalues, 109, 110, 116, 157
eigenvectors, 109, 116
Jacobi’s method, 51
Jordan canonical forms, 111
Jumps (in response), 140, 157
K
Kapitza’s pendulum, 239
Kinetic energy
of pendulum type systems, 211, 240
of vibrating beam, 15, 23
of vibrating string, 243
Kitchen experiments, 383
Kronecker’s delta, xxi
Krylov-Bogoliubov averaging, 124, 126, 239
L
Lagrange
multiplier, 21
stability, 296
Lagrange’s equations
for continuous systems, 28
for discrete systems, 20
Lagrange’s theorem, 45
Lagrangian, 21
Laminar region, 347
Laplacian operator, 485
Large rotations, 364
Limit cycle, 144, 173, 278
Limit set, 272
chaotic attractor, 272
closed orbit, 272
singular point, 272
Linear Normal Mode (LNM), 308
Lipschitzconstant, 180
continuous, 179, 180, 183
Local
analysis, 96
stability, 108, 232
Logistic map, 342
Lorenz, 324
attractor, 363
equations, 363
Lumped systems, 20
Lyapunov
dimension, 339, 451
numbers, 342
stability, 296
Lyapunov exponents, 332, 451
computing, 335, 455
defined, 332
spectrum of, 333, 369
M
Machine noise, 378
Magnetic
beam, 325, 356, 358
dipole, 366
forces, 99
Magnetoelastic ribbon, 382
Magnitude ordering (of terms), 130, 223
Mandelbrot set, 340
Manifold, 285
center, 285
invariant, 286, 351
stable, 285
sub-, 286
unstable, 285
Map
iteration of a, 367
Poincaré. See Poincaré map
Maple, 456
Marginal stability, 44, 107, 115, 296
Mass matrix, 6
Materials properties, 495
Index
523
near-elastic, 175
pendulum, 101, 368
printers, 377
state, 367
systems, 366
Imperfection, 296, 378, 438
Impulse response function, 5
Inclusion theorem, 73
Incommensurate frequencies, 293, 328
Information dimension, 339
Instationary force, 43
Instationary system, 44
Integral curve. See Orbits
Interaction, nonlinear, 209
Interface, to ODE-solver, 452
Intermittency, 345, 347, 349
route to chaos, 345
type-I, 346, 349
Internal
detuning, 218
resonance. See Resonance
Internet resources, 454
Invariant
manifold, 286, 351
mode, 308
Inverse iteration, 51
Inverse tangent bifurcations, 346
Isola, 307, 310
J
Jacobian, 108
eigenvalues, 109, 110, 116, 157
eigenvectors, 109, 116
Jacobi’s method, 51
Jordan canonical forms, 111
Jumps (in response), 140, 157
K
Kapitza’s pendulum, 239
Kinetic energy
of pendulum type systems, 211, 240
of vibrating beam, 15, 23
of vibrating string, 243
Kitchen experiments, 383
Kronecker’s delta, xxi
Krylov-Bogoliubov averaging, 124, 126, 239
L
Lagrange
multiplier, 21
stability, 296
Lagrange’s equations
for continuous systems, 28
for discrete systems, 20
Lagrange’s theorem, 45
Lagrangian, 21
Laminar region, 347
Laplacian operator, 485
Large rotations, 364
Limit cycle, 144, 173, 278
Limit set, 272
chaotic attractor, 272
closed orbit, 272
singular point, 272
Linear Normal Mode (LNM), 308
Lipschitzconstant, 180
continuous, 179, 180, 183
Local
analysis, 96
stability, 108, 232
Logistic map, 342
Lorenz, 324
attractor, 363
equations, 363
Lumped systems, 20
Lyapunov
dimension, 339, 451
numbers, 342
stability, 296
Lyapunov exponents, 332, 451
computing, 335, 455
defined, 332
spectrum of, 333, 369
M
Machine noise, 378
Magnetic
beam, 325, 356, 358
dipole, 366
forces, 99
Magnetoelastic ribbon, 382
Magnitude ordering (of terms), 130, 223
Mandelbrot set, 340
Manifold, 285
center, 285
invariant, 286, 351
stable, 285
sub-, 286
unstable, 285
Map
iteration of a, 367
Poincaré. See Poincaré map
Maple, 456
Marginal stability, 44, 107, 115, 296
Mass matrix, 6
Materials properties, 495
Index
523