Preface |
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Preface to Dynamics: Theory and Applications |
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To the Reader |
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1 Differentiation of Vectors |
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1 | (18) |
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2 | (1) |
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1.2 Direction Cosine Matrix |
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2 | (1) |
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3 | (3) |
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6 | (1) |
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1.5 Several Reference Frames |
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7 | (1) |
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7 | (2) |
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9 | (2) |
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1.8 Representations of Derivatives |
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11 | (1) |
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1.9 Notation for Derivatives |
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12 | (1) |
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1.10 Differentiation of Sums and Products |
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13 | (1) |
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14 | (1) |
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1.12 Total and Partial Derivatives |
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15 | (2) |
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1.13 Scalar Functions of Vectors |
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17 | (2) |
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19 | (20) |
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19 | (5) |
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2.2 Simple Angular Velocity |
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24 | (3) |
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2.3 Differentiation in Two Reference Frames |
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27 | (1) |
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2.4 Auxiliary Reference Frames |
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28 | (2) |
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30 | (2) |
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2.6 Velocity and Acceleration |
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32 | (2) |
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2.7 Two Points Fixed on a Rigid Body |
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34 | (1) |
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2.8 One Point Moving on a Rigid Body |
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35 | (4) |
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39 | (28) |
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3.1 Configuration Constraints |
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39 | (3) |
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3.2 Generalized Coordinates |
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42 | (2) |
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3.3 Number of Generalized Coordinates |
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44 | (1) |
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45 | (3) |
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48 | (3) |
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3.6 Partial Angular Velocities, Partial Velocities |
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51 | (4) |
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3.7 Motion Constraints with Nonlinear Equations |
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55 | (2) |
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3.8 Partial Angular Accelerations, Partial Accelerations |
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57 | (3) |
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3.9 Acceleration and Partial Velocities |
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60 | (7) |
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67 | (33) |
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67 | (2) |
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4.2 Curves, Surfaces, and Solids |
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69 | (2) |
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4.3 Inertia Vector, Inertia Scalars |
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71 | (3) |
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4.4 Mutually Perpendicular Unit Vectors |
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74 | (2) |
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4.5 Inertia Matrix, Inertia Dyadic |
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76 | (5) |
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4.6 Parallel Axes Theorems |
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81 | (2) |
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4.7 Evaluation of Inertia Scalars |
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83 | (4) |
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4.8 Principal Moments of Inertia |
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87 | (10) |
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4.9 Maximum and Minimum Moments of Inertia |
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97 | (3) |
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100 | (34) |
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5.1 Moment about a Point, Bound Vectors, Resultant |
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100 | (4) |
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104 | (1) |
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5.3 Equivalence, Replacement |
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105 | (4) |
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5.4 Generalized Active Forces |
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109 | (4) |
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5.5 Forces Acting on a Rigid Body |
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113 | (3) |
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5.6 Contributing Interaction Forces |
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116 | (2) |
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5.7 Terrestrial Gravitational Forces |
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118 | (4) |
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5.8 Coulomb Friction Forces |
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122 | (6) |
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5.9 Generalized Inertia Forces |
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128 | (6) |
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6 Constraint Forces, Constraint Torques |
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134 | (29) |
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6.1 Constraint Equations, Acceleration, Force |
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134 | (2) |
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6.2 Holonomic Constraint Equations |
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136 | (2) |
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6.3 Linear Nonholonomic Constraint Equations |
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138 | (2) |
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6.4 Nonlinear Nonholonomic Constraint Equations |
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140 | (2) |
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6.5 Constraint Forces Acting on a Rigid Body |
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142 | (6) |
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6.6 Noncontributing Forces |
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148 | (10) |
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6.7 Bringing Noncontributing Forces into Evidence |
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158 | (5) |
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163 | (28) |
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163 | (10) |
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7.2 Potential Energy Contributions |
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173 | (5) |
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7.3 Dissipation Functions |
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178 | (1) |
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179 | (3) |
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7.5 Homogeneous Kinetic Energy Functions |
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182 | (2) |
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7.6 Kinetic Energy and Generalized Inertia Forces |
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184 | (7) |
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8 Formulation of Equations of Motion |
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191 | (49) |
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191 | (8) |
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8.2 Secondary Newtonian Reference Frames |
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199 | (3) |
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8.3 Additional Dynamical Equations |
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202 | (3) |
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8.4 Linearization of Dynamical Equations |
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205 | (8) |
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8.5 Systems at Rest in a Newtonian Reference Frame |
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213 | (4) |
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217 | (3) |
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8.7 Motions Resembling States of Rest |
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220 | (3) |
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8.8 Generalized Impulse, Generalized Momentum |
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223 | (6) |
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229 | (11) |
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9 Extraction of Information from Equations of Motion |
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240 | (66) |
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9.1 Integrals of Equations of Motion |
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240 | (3) |
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243 | (3) |
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9.3 The Checking Function |
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246 | (8) |
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254 | (7) |
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9.5 Exact Closed-Form Solutions |
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261 | (4) |
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9.6 Numerical Integration of Differential Equations of Motion |
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265 | (12) |
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9.7 Determination of Constraint Forces and Constraint Torques |
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277 | (5) |
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9.8 Real Solutions of a Set of Nonlinear, Algebraic Equations |
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282 | (7) |
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9.9 Motions Governed by Linear Differential Equations |
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289 | (17) |
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10 Kinematics of Orientation |
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306 | (47) |
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306 | (3) |
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309 | (8) |
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317 | (9) |
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326 | (5) |
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10.5 Wiener-Milenkovic Parameters |
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331 | (3) |
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10.6 Angular Velocity and Direction Cosines |
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334 | (2) |
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10.7 Angular Velocity and Orientation Angles |
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336 | (5) |
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10.8 Angular Velocity and Euler Parameters |
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341 | (4) |
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10.9 Angular Velocity and Wiener-Milenkovic Parameters |
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345 | (8) |
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353 | (130) |
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Problem Set 1 (Sees. 1.1--1.13) |
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353 | (4) |
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Problem Set 2 (Sees. 2.1--2.5) |
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357 | (6) |
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Problem Set 3 (Sees. 2.6--2.8) |
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363 | (8) |
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Problem Set 4 (Sees. 3.1--3.9) |
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371 | (9) |
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Problem Set 5 (Sees. 4.1--4.5) |
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380 | (5) |
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Problem Set 6 (Sees. 4.6--4.9) |
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385 | (4) |
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Problem Set 7 (Sees. 5.1--5.3) |
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389 | (3) |
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Problem Set 8 (Sees. 5.4--5.9) |
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392 | (11) |
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Problem Set 9 (Sees. 6.1--6.7) |
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403 | (7) |
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Problem Set 10 (Sees. 7.1--7.3) |
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410 | (6) |
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Problem Set 11 (Sees. 7.4--7.6) |
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416 | (4) |
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Problem Set 12 (Sees. 8.1--8.3) |
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420 | (10) |
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Problem Set 13 (Sees. 8.4--8.9) |
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430 | (10) |
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Problem Set 14 (Sees. 9.1--9.6) |
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440 | (9) |
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Problem Set 15 (Sees. 9.7--9.9) |
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449 | (19) |
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Problem Set 16 (Sees. 10.1--10.5) |
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468 | (7) |
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Problem Set 17 (Sees. 10.6--10.9) |
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475 | (8) |
Appendix I Direction Cosines as Functions of Orientation Angles |
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483 | (5) |
Appendix II Kinematical Differential Equations in Terms of Orientation Angles |
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488 | (5) |
Appendix III Inertia Properties of Uniform Bodies |
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493 | (12) |
Index |
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505 | |