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Featherstone R. — Rigid Body Dynamics Algorithms
Featherstone R. — Rigid Body Dynamics Algorithms

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Название: Rigid Body Dynamics Algorithms

Автор: Featherstone R.

Аннотация:

Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-body dynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer shorter, simpler code that is easier to write, understand and debug, with no lose of efficiency.

Unique features include: A comprehensive collection of the best rigid body dynamics algorithms, Use of spatial (6D) vectors to greatly reduce the volume of algebra to simplify the treatment of the subject, and to simplify the computer code that implements the algorithms, Algorithms expressed both mathematically and in pseudocode for easy translation into computer programs, Source code for many algorithms available on the internet. Rigid Body Dynamics Algorithms is aimed at readers who already have some elementary knowledge of rigid-body dynamics, and are interested in calculating the dynamics of a rigid-body system. This book serves as an algorithms recipe book as well as guide to the analysis and deeper understanding of rigid-body systems.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2007

Количество страниц: 272

Добавлена в каталог: 20.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E^n$      7 48
$FD(\cdots)$      2 41
$FD_x(\cdots)$      42
$F^3$      37 38
$F^6$      14 17 18 23 38 43
$F^n$      7 40 43 49
$ID(\cdots)$      2 41 89 103 165 173
$ID_\delta(\cdots)$      103 173
$ID_\delta(\cdots)$ pseudocode      104
$M^3$      37 38
$M^6$      11 17 18 23 38 43
$M^n$      7 40 43 49
$O(nd^2)$ vs. $O(n^3)$      102 116 206
$O(N_B) = O(n)$      90
$O(\cdots)$      90
$qdfn(\cdots)$      41
$rotx(\theta)$      23 244
$roty(\theta)$      23 244
$rotz(\theta)$      23 244
$rx(\theta)$      23 244
$ry(\theta)$      23 244
$rz(\theta)$      23 244
$R^n$      7
Absolute coordinates      74 196
Acceleration bias $(b^A)$      122 124 136 138
Acceleration bias (b)      36 58
Acceleration classical      30 97 99
Acceleration closed-form expression      92
Acceleration contact separation      214 217 221
Acceleration generalized $(\ddot{q})$      40 43—45
Acceleration generalized $(\ddot{y})$      44—46
Acceleration generalized $(\dot{\alpha})$      41
Acceleration gravitational $(a_g)$      94 181 182 185
Acceleration joint $(a_J)$      30 55 61
Acceleration joint $(c_J)$      55 83 85 95
Acceleration joint $(\ddot{q})$      55 58
Acceleration joint-space      31
Acceleration of body in system      30
Acceleration spatial      19 28—31
Acceleration time-dependent $(\overset{\circ}{\sigma})$      55
Acceleration velocity-product $(a^vp)$      144 153 182
Acceleration velocity-product (c)      126 128 131
Acceleration, summation of      30
Accelerationrelative      184
Algorithm complexity      89—90
Articulated body      120
Articulated body alternative versions      131
Articulated body as rigid-body system      123
Articulated body box-cylinder example      122
Articulated body divide and conquer      136
Articulated body equations and pseudocode      132
Articulated body floating base      181
Articulated body floating base pseudocode      182
Articulated body hybrid dynamics      176
Articulated body hybrid dynamics pseudocode      178
Articulated body hybrid dynamics table of equations      177
Articulated body multiple handles      122 136—139
Articulated body pairwise assembly      125 137
Articulated body, handle of      120 139
Articulated-body algorithm      128—131 251
Articulated-body inertia      119—128
Articulated-body inertia $I^a$ and $p^a$      127 176
Articulated-body inertia arithmetic      247 251
Articulated-body inertia basic properties      120
Articulated-body inertia calculation of assembly method      125—128
Articulated-body inertia calculation of assembly, multiple handles      136—139
Articulated-body inertia calculation of projection method      123—125
Articulated-body inertia calculation of systematic      131—136
Articulated-body inertia calculation of table of formulae      134—135
Articulated-body inertia inverse      121 124 137
Articulated-body inertia multi-handle      122 137
Articulated-body inertia properties of inverse      124
Articulated-body inertia, summation of      121
Augmented body      192
Axial-screw transform      204 249—252
Axial-screw transform table of costs      249
Base coordinates      74
Basis      see also coordinate system
Basis dual      8 17
Basis on a subspace      47
Basis orthonormal      9 11 14
Basis planar      37
Basis Plucker      11 14 24
Basis reciprocity      9 17
Baumgarte stabilization      145—147
Block-diagonal structure of K and G      158
Body $\leftrightarrow$ joint mapping (P)      61 167
Body coordinate frame $(F_i)$      73
Body coordinates      74 95 106 131
Body Jacobian      see Jacobian
Body position      74 75
Branch-induced sparsity      110—112 151 175 206
Cartesian frame      11 14 20 73
Child sets $(\mu)$      72
Closed-loop system      69 141
Closed-loop system configuration ambiguity      160
Closed-loop system mobility      159
Closed-loop system overconstraint      161
Closed-loop system, properties of      159—161
Coeffcient of restitution      233
Collision      223 228 232
Compliant contact      235—239
Composite-rigid-body algorithm      104—108
Composite-rigid-body algorithm alternative derivation      108—110
Composite-rigid-body algorithm floating base      182
Composite-rigid-body algorithm floating base pseudocode      183
Composite-rigid-body algorithm hybrid dynamics      173—176
Composite-rigid-body algorithm hybrid dynamics pseudocode      174
Composite-rigid-body algorithm hybrid dynamics sparsity      175
Composite-rigid-body algorithm operations-count analysis      204—208
Composite-rigid-body algorithm pseudocode      107
Computational cost      see efficiency
Condition number      198 201
Configuration space      40
Connectivity      66—72
Connectivity graph      66—72
Connectivity graph for hybrid dynamics      175
Connectivity graph representation      71—72
Connectivity graph spanning tree      67
Connectivity graph, expansion of      114
Constraint      see motion force inequality
Contact constraint equation      215 217 223
Contact dynamics      213—222 236
Contact dynamics having no solution      218
Contact dynamics simulation procedure      225
Contact normal      213 216 220
Contact normal joint space      220
Coordinate system Cartesian      11 14
Coordinate system dual      9 17 40
Coordinate system generalized      40 43 59
Coordinate system homogeneous      22
Coordinate system Plucker      11 15—16 20 43
Coordinate transform      9 18
Coordinate transform .apply()      246 248
Coordinate transform .invApply()      246 248
Coordinate transform homogeneous      22
Coordinate transform how to describe      23 241
Coordinate transform planar      38 241
Coordinate transform Plucker      20—23
Coordinate transform rotation      21 243
Coordinate transform table of formulae      23 244
Coordinate transform translation      21 243
Couple      see force
Cross product      23—25 243
Cross product dual $(\times^*)$      23 25
Cross product operator form $(a\times)$      9 21 25
Cross product operator form $(a\times^*)$      25
Cross product planar      37 241
Cross product table of properties      22 25
Cross productas differential operator      23
Decomposition of vectors      47 50
Denavit — Hartenberg (DH) parameters      75—77
Denavit — Hartenberg coordinate frame      75 204 207 250
Derivative apparent      27 30 55
Derivative componentwise      26
Derivative of a coordinate transform      28
Derivative of a Plucker basis vector      23
Derivative of a vector      25
Derivative of inertia      33
Differentiation      25—27
Differentiation dot notation $(\dot{v})$      26 27
Differentiation in moving coordinates      26
Differentiation ring notation $(\overset{\circ}{v})$      27
Differentiation table of formulae      26
Direct sum $(\oplus)$      48
Dyad      10 33
Dyadic      10 33—34
Dyadic table of properties      34
Dynamic equivalence      189
Dynamics algorithms      1
Dynamics algorithms model—based      3 65 209
Efficiency      201—204
Efficiency branched trees      206—208
Efficiency comparison between algorithms      201—204
Efficiency optimization      204—206
Efficiency symbolic simplification      209—212
Efficiency tricks      252—256
Efficiency, measure of      201
Equation of motion articulated-body      120—122 124 176
Equation of motion closed form      92
Equation of motion closed-loop inverse dynamics      165
Equation of motion closed-loop system      142 143 150 152
Equation of motion constrained rigid body      57—60 215 217
Equation of motion contact dynamics      215 217 221
Equation of motion contact dynamics, solution of      224—227
Equation of motion floating base      180 181
Equation of motion general      2 40—42 44 59 102 219
Equation of motion impulsive      231
Equation of motion multiple bodies      60
Equation of motion projected      46 124 152
Equation of motion rigid body      3 19 35—36
Equation of motion spanning tree      142
Equation of motion state-space formulation      42
Equation of motion two-body system      190
Equation of motion with explicit constraints      45
Equation of motion with gear constraints      188
Equation of motion with implicit constraints      45 59 63 143 150 167
Equation of motion, collection of      43
Equation of motion, construction of      42—46
Equation of motion, inconsistency in      150
Euler angles      84
Euler parameters      86
Euler's equation      36
Excess mobility      161
Factorization      see sparse matrix
First-order dynamical system      235
Fixed base      66 74
Floating base      67 179
Floating-base coordinates      156 179—182
Floating-base forward dynamics      181—183
Floating-base inverse dynamics      183—185
Floating-base inverse dynamics equations and pseudocode      185
Floating-base system      156 179—181
Floating-point arithmetic      197
Floating-point operations count      201
Floating-point operations count for published algorithms      202
Floating-point operations count, graph of      203 209
Force acting on body i      93
Force action and reaction      18
Force actuator      165—166
Force angular (couple)      14
Force bias $(p^A)$      120 124 127
Force bias $(p^c)$      180 184
Force bias (C)      40 59 103 152—154
Force bias (p)      35 57
Force constraint $(f_c)$      57
Force constraint $(\lambda)$      44 54 59 63 150—151 167
Force constraint $(\tau_c)$      44
Force contact $(f_c)$      214 216
Force contact $(\lambda)$      217
Force contact $(\tau_c)$      220
Force Coriolis and centrifugal      40 94
Force external $(f^x)$      93 153 167
Force generalized $(\tau)$      40 54 59
Force generalized (u)      46
Force gravitational      35 40 57
Force hybrid bias (C')      173
Force joint $(f_J)$      53 62
Force joint $(\tau)$      54 63
Force linear      13
Force loop joint      142 148—149
Force loop joint active $(\tau^a, f^a)$      148 152—154
Force loop joint constraint $(\tau^c, \lambda)$      143 149
Force moment about point      14
Force soft contact      236
Force spatial      13—15
Force subspace matrix active      54 56 63 153
Force subspace matrix constraint      54 56 58 62 143 155 167
Force, summation of      18
Forward dynamics      2 41 101 117 119
Forward dynamics joint set (fd)      172
Friction      233 238
Friction, coefficient of      239
Gauss' principle of least constraint      225
Gears      55 81 186—189
Geometric event      228
Geometry contact      227—230
Geometry system model      73—74 77
Gravity      see force acceleration
Gravity compensation      94
Handle      see articulated body
Hybrid dynamics      171—176
impact      213 232
Impulse      214 230
Impulsive dynamics      230—235
Inequality constraint      222—223
Inequality constraint, possible states of      222
Inertia articulated-body      see articulated-body inertia
Inertia composite-rigid-body      105 184
Inertia generalized      40 59
Inertia inverse      36—37 50 58
Inertia joint-space      102—103 105
Inertia of geared electric motor      189
Inertia parameters      189—193
Inertia parameters modification $(I_\Delta)$      190
Inertia parameters modification $(I_\Delta)$ table of values      191
Inertia parameters simplification      192
Inertia planar      38 242
Inertia rigid-body      32 35 243 250
Inertia rotational      31 33
Inertia spatial      33—35
Inertia, properties of      34
Inverse dynamics      2 41 89 99 164—166 183—185
Jacobian body      20 31 73 124 144 220 232
Jacobian floating-base      186
Jacobian loop      145 148
Jcalc$(\cdots)$      see joint calculation function
Joint      39 53 65
Joint 6-DoF      67 78 179
Joint axis vector      20 30 91
Joint bearings      56 94
Joint calculation function      80 83 146 154
Joint constraint      see motion constraint
Joint cylindrical      52 78 147 148
Joint helical (screw)      77 78
Joint location frame $(F_{i,j})$      74
Joint model      78—80
Joint model library      78
Joint model table of formulae      78 148
Joint parameter      80 82
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