Featherstone R. — Rigid Body Dynamics Algorithms :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

Joint planar      78 81
Joint polarity      69
Joint polarity, reversal of      83
Joint prismatic      20 52 77 78 148 191
Joint rack and pinion      81
Joint revolute      20 55 77 78 148 191
Joint sphere-in-cylinder      161
Joint spherical      78 84 86 148 191
Joint symmetry      70 83
Joint transform       74 82 147
Joint type descriptor      78 83
Joint variable      20 30 53 77 81 84 86
Joint zero-DoF      147 148
Joint-space inertia matrix      see inertia
Jourdain's principle      44
Jtype(i)      see joint type descriptor
Kinematic chain      19 30 69 75 91
Kinematic constraint      see motion constraint
Kinematic loop      68 141
Kinematic loop closed-form solution      164
Kinematic loop independent      68
Kinematic loop, number of      68
Kinematic tree      67
Kinematic tree floating      125
Kinematic tree unbranched      see kinematic chain
kinetic energy      32 35 40 46 104 105 186
Lagrange multiplier      44
Lie algebra      38
Line contact      229
Linear complementarity problem (LCP)      224
Link      67
Link coordinates      see body coordinates
Loop closure function      see motion constraint
Loop constraint      see motion constraint
Loop joint      69 142 144 146 147
Loop joint passive      142
Loop joint universal      147
Loop position error $(\delta)$       146—148 155
Mass      31
Mass apparent      121 123
Mass apparent, centre of      121 123
Mass, centre of      31 32 36
Minimal loop cluster      158
Modelling error      199
Momentum angular      31
Momentum linear      31
Momentum moment about point      31
Momentum of floating-base system      185
Momentum spatial      19 31—32
Motion constraint      44—46 50—53
Motion constraint classification hierarchy      51
Motion constraint explicit      44—46 161
Motion constraint holonomic      50
Motion constraint implicit      44 45 55 62 143
Motion constraint joint      53—55
Motion constraint loop closure      143—145 154—156
Motion constraint loop closure function      161—164
Motion constraint loop closure function example      162
Motion constraint loop closure pseudocode      155
Motion constraint loop closure rounding-error problem      156
Motion constraint nonholonomic      50
Motion constraint rheonomic      51
Motion constraint scleronomic      51
Motion constraint three-body      52
Motion constraint, stabilization of      145—147
Motion subspace matrix      50 53 56 57 83 85 179
Motor algebra      38
Moving body      66
Newton's equation      36
Numerical integration      198 226
Orthogonal complements      48—49
Orthogonal complements table of properties      49
Overconstraint      161
Parent array $(\lambda)$       71
Parent array $(\lambda)$ expansion of      114
Parent array $(\lambda)$ for hybrid dynamics      175
Planar vector      37—38 196 241
Planar vector arithmetic functions      242
Point contact      213 216
Polyhedron      227
Power      17 19
Power balance equation      54 59
Predecessor      53 60 69 143 148 219
Predecessor array (p)      71
Predecessor array (pc)      220
Predecessor frame      78 146 154
Predecessor transform array       74
Prescribed motion      172
Prismatic      see joint
Projection method      46 123—125
Properly actuated system      166
Properly constrained system      159 161
Pruning constraint equations      150
Quadratic program      224
Quaternion      84
Radius of gyration      196
Reciprocity condition      see basis
Recurrence relations      90—92
Recursive formulation      90
Recursive Newton — Euler algorithm      92—97
Recursive Newton — Euler algorithm floating base      182
Recursive Newton — Euler algorithm floating base pseudocode      183
Recursive Newton — Euler algorithm modified for loops      153
Recursive Newton — Euler algorithm modified for loops pseudocode      154
Recursive Newton — Euler algorithm original version      97—99
Recursive Newton — Euler algorithm pseudocode      96

Redundantly actuated system      166
Reference coordinates      74 180
Regular numbering      69
Removing high-frequency dynamics      172
Restitution tangential      233 234
Restitution torsional      233 234
Restitution, coefficient of      233
Revolute      see joint
Rigid-body system      39 65
Rigid-body system crank-slider linkage      66
Rigid-body system ladder      168
Rigid-body system satellite      67
rot(E)      23
Rotation      84—86 253—256
Rotation matrix (E)      21 85 86 252
Round-off error      196—198
Scalar product      8 17—19
Scalar product nondegenerate      8
Scalar product operator form $(a\cdot)$       9
Screw axis      16
Screw theory      16 38
Sensitivity      199—201
Soft contact      see compliant contact
Solving $K\ddot{q}=k$ to get $\ddot{q}=G\ddot{y} + g$       152 156—157
Spanning tree      43 141—142
Spanning tree minimum-depth      201
Sparse matrix algorithms      112—116
Sparse matrix algorithms       111
Sparse matrix algorithms       112
Sparse matrix algorithms       112 151
Sparse matrix algorithms back-substitution      115
Sparse matrix algorithms Cholesky      111
Sparse matrix algorithms multiplication      115
Sparse matrix algorithms, computational cost of      116
Sparse matrix method      166—168
Sparsity in K and G      158—159
Spatial vector      3 7 40
Spatial vector arithmetic      243—252
Spatial vector arithmetic compact data structures      245
Spatial vector arithmetic simple functions      244
Spatial vector arithmetic table of operations      247
Spatial vector arithmetic type safety      246
Spatial vector force      8 18
Spatial vector magnitude      17
Spatial vector motion      8 18
Spatial vector unit      17
Spatial vector, use of      18—19
State space      42
Subtree sets $(\nu)$       72 174
Successor      53 60 69 143 148 219
Successor array (s)      71
Successor array (sc)      220
Successor frame      78 146 154
Successor transform array       74
Support      72
Support sets $(\kappa)$       72
Surface contact      229
Symbolic simplification      see efficiency
System model      2 41 65 87
Tensor      see dyadic inertia
Topological tree      67
topology      see connectivity
Tree joint      69
Tree joint in forward direction      71
Tree joint in reverse direction      71 83
Tree transform array       74 77
Truncation error      198
Twist      16
Underactuated system      166
Unilateral constraint      222
Units (measurement)      4
Vector      7
Vector 3D      3 8
Vector abstract      8
Vector coordinate      8
Vector Euclidean      8 48
Vector field      12
Vector free      16
Vector line      16
Vector planar      see planar vector
Vector space      7
Vector space, dual of      8 17
Vector spatial      see spatial vector
Vector subspace      46—50
Vector subspace active force      54 56
Vector subspace constraint force      49 54 57
Vector subspace matrix representation      47
Vector subspace motion      46 49 53 57
Velocity angular      10
Velocity bias $(\sigma)$       53—55 143
Velocity contact separation      214 216 220
Velocity generalized $(\alpha)$       41
Velocity generalized $(\dot{q})$       40
Velocity generalized $(\dot{y})$       44
Velocity joint       19 53 61 80 82 95 143
Velocity joint $(\alpha)$       81
Velocity joint $(\dot{q})$       53
Velocity joint-space      20
Velocity linear      10
Velocity of body in system      20 72 80
Velocity of point in body      10
Velocity relative      18
Velocity spatial      10—13
Wrench      16
xlt(r)      23 244
XtoV      242 243
Zero-dimensional matrix      53

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