tumbling, 366
universal routes, 341
weak, 325
Chaos-criteria, 348
Chirikov’s overlap, 362
conservative chaos, 362
heuristic, 356, 358
homoclinic tangles, 350
intermittency, 349
Melnikov, 353
perturbation-based, 358, 360
Smale horseshoes, 350
sufficient, 356, 371, 375
transient chaos, 349
Chaotic
attractor, 334
autoparametric systems, 372
bursts, 345, 347, 349
coupled autonomous systems, 369
Duffing systems, 363
dynamics, 323
high-order systems, 376
intermittency, 345
pendulum systems, 364
piecewise linear systems, 366
space ball, 383
vibrations, 323
windows, 345
Characteristic polynomial, 51, 82
Chelomei’s pendulum, 238, 264, 438, 445
Chirikov’s overlap criterion, 362
Circulatory
force, 43
system, 44
Codimension, 274
Codimension one bifurcation, 271, 274, 280,
292, 293, 316
Codimension two bifurcation, 274, 292, 294
Coefficient of restitution, 176, 177, 181, 188,
368
Collocation, 84
Combination resonance, 132
Commensurate frequencies, 210
Commuting matrices, 50
Comparison
eigenvalue problem, 71
function, 27, 64
theorem, 71
Completely definite EVP, 65
Completely dissipative force, 43
Complex conjugated, 477
Complex numbers, 477
Complex-valued
eigenvalues, 18
mode shapes, 18
Composite systems, 85
Computational dynamics, 449
Configuration plot, 309
Conservative chaos, 362
Conservative force, 43
Conservative system, 44
Constraints, 21, 22
Continuation
arclength, 157, 299, 304
control-based, 141, 306
in lab experiments, 304
natural parameter, 298
numerical, 298
pseudo-arclength, 141
sequential, 298
Continuous bifurcation, 294
Contracting phase space, 334
Control
by HF excitation, 435, 462
closed-loop, 457
dither, 435, 462
dynamic, 377
feedback, 364, 457
of chaos, 381
of stiffness, 457
of systems, 364
open-loop, 457
structural, 100
tension, 364, 377, 457
Control-based continuation, 141, 306
Coriolis acceleration, 241
Correlation dimension, 339
Coulomb friction, 99, 398, 419
Creep, 378
Critical
state, 145
value, 145, 273, 276, 294
variable, 287
velocity, 359
Curvature, 56, 97
D
D’Alembert’s Principle, 38
Damping
critical, 3
generalized, 17
mass-proportional, 9, 17, 18, 36
matrix, 6
measures, 33
models, 32
negative, 171, 172
nonlinear, 99, 171, 364
non-proportional, 18
Index
519
universal routes, 341
weak, 325
Chaos-criteria, 348
Chirikov’s overlap, 362
conservative chaos, 362
heuristic, 356, 358
homoclinic tangles, 350
intermittency, 349
Melnikov, 353
perturbation-based, 358, 360
Smale horseshoes, 350
sufficient, 356, 371, 375
transient chaos, 349
Chaotic
attractor, 334
autoparametric systems, 372
bursts, 345, 347, 349
coupled autonomous systems, 369
Duffing systems, 363
dynamics, 323
high-order systems, 376
intermittency, 345
pendulum systems, 364
piecewise linear systems, 366
space ball, 383
vibrations, 323
windows, 345
Characteristic polynomial, 51, 82
Chelomei’s pendulum, 238, 264, 438, 445
Chirikov’s overlap criterion, 362
Circulatory
force, 43
system, 44
Codimension, 274
Codimension one bifurcation, 271, 274, 280,
292, 293, 316
Codimension two bifurcation, 274, 292, 294
Coefficient of restitution, 176, 177, 181, 188,
368
Collocation, 84
Combination resonance, 132
Commensurate frequencies, 210
Commuting matrices, 50
Comparison
eigenvalue problem, 71
function, 27, 64
theorem, 71
Completely definite EVP, 65
Completely dissipative force, 43
Complex conjugated, 477
Complex numbers, 477
Complex-valued
eigenvalues, 18
mode shapes, 18
Composite systems, 85
Computational dynamics, 449
Configuration plot, 309
Conservative chaos, 362
Conservative force, 43
Conservative system, 44
Constraints, 21, 22
Continuation
arclength, 157, 299, 304
control-based, 141, 306
in lab experiments, 304
natural parameter, 298
numerical, 298
pseudo-arclength, 141
sequential, 298
Continuous bifurcation, 294
Contracting phase space, 334
Control
by HF excitation, 435, 462
closed-loop, 457
dither, 435, 462
dynamic, 377
feedback, 364, 457
of chaos, 381
of stiffness, 457
of systems, 364
open-loop, 457
structural, 100
tension, 364, 377, 457
Control-based continuation, 141, 306
Coriolis acceleration, 241
Correlation dimension, 339
Coulomb friction, 99, 398, 419
Creep, 378
Critical
state, 145
value, 145, 273, 276, 294
variable, 287
velocity, 359
Curvature, 56, 97
D
D’Alembert’s Principle, 38
Damping
critical, 3
generalized, 17
mass-proportional, 9, 17, 18, 36
matrix, 6
measures, 33
models, 32
negative, 171, 172
nonlinear, 99, 171, 364
non-proportional, 18
Index
519