Index
a
- absolute nodal coordinate approach 265
- acceleration 82
- ADMAS 8
- amplitude resonance 72
- angle 12, 15–17, 84
- angular acceleration 183, 184
- angular displacement 8, 15–17
- angular velocity 12, 207, 225, 243
- ANSYS 2
- applied force 591
- assumed modes method 11
- attack angle 12, 578, 579
- augmented eigenvector 6–10, 17, 86–115
- augmented operator 6, 7, 14, 17, 87
b
- beam theory 67, 296
- bending stiffness 29
- body 1
- body dynamics equation of body element 8–14, 80
- body dynamics equations of system 8–14, 79, 87
- body‐fixed coordinate system 15, 16, 185, 187, 266
- boundary conditions 31, 32
- boundary element method 2
- boundary ends 9, 15, 23, 434, 435, 442
- branch multibody system 356, 607
c
- Cartesian coordinates 144
- center of mass 579
- centrifugal force 2
- chain multi‐rigid‐flexible‐body system 100, 443
- chain system 9, 11, 23, 55, 185, 442
- characteristic equation 22, 32
- chessboard rule 378, 408–412
- classical transfer matrix method (classical TMM) 3
- closed‐loop system 129, 435, 442
- complex transfer matrix 59, 73, 404
- component mode synthesis method 270
- computational efficiency 5, 6, 8, 14
- computational scale 2, 3, 5, 10–14, 21, 22
- computer‐aided design (CAD) 4
- conjugate complex numbers 59
- conjugate operator 85
- conjugate transformation 84, 85
- constitutive relations 93, 97, 98, 100, 101, 646
- continuity assumption 270
- continuous functions 84, 87, 89
- continuous system 6, 12
- controlled multibody system 327, 348–375
- Coriolis acceleration 269
- Coriolis forces 2
- corotational coordinate approach 265
- cross‐product matrix 15
d
- damped system 22, 33, 57
- damper 2, 56
- damping coefficient 56, 58, 112, 254
- damping linear operator 113, 114
- damping ratio 21, 71, 112
- deflection angle 12, 541, 578
- degrees of freedom (DOF) 2
- dichotomy method 36
- differential‐algebraic equations 219
- discrete system 5, 11, 41
- discrete time transfer matrix method (DTTMM) 5, 183
- discrete time transfer matrix method for multibody systems (MSDTTMM) 6, 217–266
- discrete time transfer matrix method for multi‐rigid‐body systems (MRSDTTMM) 6, 217–220, 259
- discrete time transfer matrix method for multi‐rigid‐flexible‐body systems 6, 217
- displacements 22
- disturbance factors 12, 491, 493
- dynamics design 7, 12–14, 79
- dynamics response 79, 102
e
- eigenequation 9, 10, 358, 505
- eigenfrequency 21, 25, 26, 33, 40, 89
- eigenfunctions 87, 96, 107
- eigenvalue problem 5, 7, 14, 21, 22
- eigenvector orthogonality 2
- elastic coefficient 105, 329, 336, 346, 583, 622
- elastic force 60, 154, 329, 557, 646
- entire elasticity assumption 271
- equation of motion 60
- Euclidean space 84, 85
- Euler–Bernoulli beam 41, 44–53
- Eulerian formula 59
- extended MSTMM 8, 120
- extended state vectors 68, 73, 122, 134
- extended transfer equation 63, 64, 72, 122, 350, 404
- extended transfer matrix 73, 74, 120, 350, 396–401
- exterior ballistics 12, 517, 518
f
- finite difference 167
- finite element method (FEM) 1
- finite element transfer matrix method 5, 140–153
- finite element transfer matrix method for a multibody system (FE‐MSTMM) 129, 338
- finite segment discrete time transfer matrix method for multibody systems 341
- finite segment method 265, 341, 342
- firing dispersion 6, 489
- firing frequency 21, 504
- firing orders 21
- firing precision 21, 489
- firing sequence 492, 519
- flexible body 1, 2, 199
- floating frame of reference formulation 199, 266
- forced vibration 63
- forced vibration systems 378
- Fourier coefficients 130, 132
- Fourier series 120, 130–132, 162
- framework system 129
- free end 50
- free vibration 25, 40
g
h
i
- ideal trajectory 12
- ill‐condition 2, 5, 7, 11, 13, 14, 21, 22, 140
- inboard body 14, 189
- incremental method 131
- incremental TMM 130
- incremental transfer matrix 131, 134
- inertia coordinate system 23, 266, 267, 683
- initial condition 10
- initial disturbance 12, 489
- inner product space 83
- input end 15, 24
- interior ballistic 12, 517, 548
- internal forces 15
- internal moments 32, 34, 82, 189–193, 206
- International System of Units (SI) 17
- isotropy assumption 271
j
k
l
- Lagrange equation 146, 148
- Lagrange interpolation polynomial 228
- Lagrange multipliers 219
- Lagrangian equations 219
- large motion 1
- launch dispersion 13
- launch dynamics 1, 12
- launch dynamics of multibody systems 5
- launching frequency 7
- launch system 2, 3, 5–7, 12–14
- light damped system 58
- linearization 225
- linear multibody system dynamics 21, 79
- linear operator 81, 82, 85, 113, 114
- linear space 83, 84, 86
- linear system 3, 14, 15
- linear time‐invariant multibody systems 225, 607
- linear transformation 4, 85
- longitudinal stiffness 88, 646
- longitudinal vibration 23, 26–28
- lumped mass 1, 27
m
- Marting’s equation 514
- modal analysis method 13, 21, 79, 265, 276, 277, 305, 318
- modal coordinates 6, 16, 22, 26
- modal synthesis method 2, 7, 13, 21
- mode superposition method 40, 114
- multibody system (MS) 1
- multibody system dynamics (MSD) 1
- multi‐degree‐of‐freedom system 138
- multi‐flexible‐body system (MFS) 2, 21, 199
- multi‐flexible‐body system dynamics (MFSD) 2
- multiple launch rocket system (MLRS) 3, 491
- multi‐rigid‐body system (MRS) 1, 183
- multi‐rigid‐body system dynamics (MRSD) 1
- multi‐rigid‐flexible‐body system (MRFS) 1
- multi‐rigid‐flexible‐body systems dynamics (MRFSD) 80
- multi‐rigid‐launch‐body systems dynamics (MRLSD) 79
n
o
p
- parameter matrix 80
- parameter matrix of damping 80
- parameter matrix of mass 80
- parameter matrix of stiffness 80
- partial differential equations 10
- phase resonance 72
- physical coordinates 6, 15–17
- planar motion 25
- potential energy 147
- principal coordinates 8, 40
- principal modals 25
- principal mode shape 40
- principal vibration 40
q
- quasi‐linear system 130
r
- Rayleigh–Ritz method 265, 269
- real trajectory 12
- Riccati discrete time transfer matrix method for multibody systems (Riccati MSDTTMM) 6, 423–429
- Riccati finite element transfer matrix method 417
- Riccati transfer matrix method (Riccati TMM) 3, 154, 417
- Riccati transfer matrix method for multibody systems (Riccati MSTMM) 378, 417
- Riccati transformation 8, 158, 418
- rigid body 1
- Runge–Kutta method 108
s
- self‐propelled artillery 3, 545
- shape function 146
- Shear deformations 142
- shipboard gun 489
- simple‐harmonic excitation 63
- simple harmonic external force 349
- small deformation assumption 199, 271
- smooth hinge 14, 225
- spatial motion 41, 269, 274
- spin angle 12
- state variables 6, 22
- state vector 22–26, 184, 200, 222–224, 276
- static response 80, 124
- steady‐state oscillations 139
- steady‐state response 7, 63
- steady‐state vibration 63
- step‐by‐step scanning method 36
- step‐by‐step time integration method 225
- stiffness gradient 2
- stiffness matrix 5, 146, 147, 154, 339, 340, 377
- structural damping 56, 72
- structural dynamics 3
- swing angle 12, 518
- symmetric transformation 84
- symmetry operator 85
t
- Taylor expansion theorem 226
- Timoshenko beam 41, 390
- topology figure 433–436
- torsional stiffness 48
- torsional vibration 3
- transfer direction 15
- transfer equations 9, 26
- transfer matrix 3, 26
- transfer matrix library 12, 377, 607
- transfer matrix method (TMM) 3
- transfer matrix method for linear multibody systems 22
- transfer matrix method for multibody systems (MSTMM) 3, 5
- transient response 63, 102
- transpose transformation 85
- transverse vibration 3, 29
- tree system 129, 435
- trigonometric series 165
- two‐dimensional system 5, 140, 162, 167, 170
- two‐phase flow 548, 563, 565
u
v
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