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<p>Preface xi</p> <p>About the Companion Website xv</p> <p><b>Part I Modeling: Deriving Equations of Motion </b><b>1</b></p> <p><b>1 Kinematics </b><b>3</b></p> <p>1.1 Derivatives of Vectors 3</p> <p>1.2 Performing Kinematic Analysis 5</p> <p>1.3 Two Dimensional Motion with Constant Length 6</p> <p>1.4 Two Dimensional Motion with Variable Length 8</p> <p>1.5 Three Dimensional Kinematics 10</p> <p>1.6 Absolute Angular Velocity and Acceleration 13</p> <p>1.7 The General Acceleration Expression 14</p> <p>Exercises 16</p> <p><b>2 Newton’s Equations of Motion </b><b>19</b></p> <p>2.1 The Study of Motion 19</p> <p>2.2 Newton’s Laws 19</p> <p>2.3 Newton’s Second Law for a Particle 20</p> <p>2.4 Deriving Equations of Motion for Particles 21</p> <p>2.5 Working with Rigid Bodies 25</p> <p>2.6 Using <i>F </i>= <i>ma </i>in the Rigid Body Force Balance 26</p> <p>2.7 Using <i>F </i>= d<i>G/</i>d<i>t </i>in the Rigid Body Force Balance 28</p> <p>2.8 Moment Balance for a Rigid Body 30</p> <p>2.9 The Angular Momentum Vector – <i>H_O </i>33</p> <p>2.10 A Physical Interpretation of Moments and Products of Inertia 36</p> <p>2.11 Euler’s Moment Equations 40</p> <p>2.12 Throwing a Spiral 41</p> <p>2.13 A Two Body System 42</p> <p>2.14 Gyroscopic Motion 48</p> <p>Exercises 52</p> <p><b>3 Lagrange’s Equations of Motion </b><b>55</b></p> <p>3.1 An Example to Start 55</p> <p>3.2 Lagrange’s Equation for a Single Particle 58</p> <p>3.3 Generalized Forces 62</p> <p>3.4 Generalized Forces as Derivatives of Potential Energy 64</p> <p>3.5 Dampers – Rayleigh’s Dissipation Function 65</p> <p>3.6 Kinetic Energy of a Free Rigid Body 67</p> <p>3.7 A Two Dimensional Example using Lagrange’s Equation 70</p> <p>3.7.1 The Kinetic Energy 70</p> <p>3.7.2 The Potential Energy 71</p> <p>3.7.3 The <i>𝜃 </i>Equation 72</p> <p>3.7.4 The <i>𝜙 </i>Equation 73</p> <p>3.8 Standard Form of the Equations of Motion 73</p> <p>Exercises 74</p> <p><b>Part II Simulation: Using the Equations of Motion </b><b>77</b></p> <p><b>4 Equilibrium Solutions </b><b>79</b></p> <p>4.1 The Simple Pendulum 79</p> <p>4.2 Equilibrium with Two Degrees of Freedom 80</p> <p>4.3 Equilibrium with Steady Motion 81</p> <p>4.4 The General Equilibrium Solution 84</p> <p>Exercises 85</p> <p><b>5 Stability </b><b>87</b></p> <p>5.1 Analytical Stability 87</p> <p>5.2 Linearization of Functions 92</p> <p>5.3 Example: A System with Two Degrees of Freedom 95</p> <p>5.4 Routh Stability Criterion 99</p> <p>5.5 Standard Procedure for Stability Analysis 103</p> <p>Exercises 105</p> <p><b>6 Mode Shapes </b><b>107</b></p> <p>6.1 Eigenvectors 107</p> <p>6.2 Comparing Translational and Rotational Degrees of Freedom 111</p> <p>6.3 Nodal Points in Mode Shapes 115</p> <p>6.4 Mode Shapes with Damping 116</p> <p>6.5 Modal Damping 118</p> <p>Exercises 122</p> <p><b>7 Frequency Domain Analysis </b><b>125</b></p> <p>7.1 Modeling Frequency Response 125</p> <p>7.2 Seismic Disturbances 132</p> <p>7.3 Power Spectral Density 133</p> <p>7.3.1 Units of the PSD 138</p> <p>7.3.2 Simulation using the PSD 139</p> <p>Exercises 143</p> <p><b>8 Time Domain Solutions </b><b>145</b></p> <p>8.1 Getting the Equations of Motion Ready for Time Domain Simulation 146</p> <p>8.2 A Time Domain Example 147</p> <p>8.3 Numerical Schemes for Solving the Equations of Motion 149</p> <p>8.4 Euler Integration 149</p> <p>8.5 An Example Using the Euler Integrator 151</p> <p>8.6 The Central Difference Method: An (<i>h</i>2) Method 153</p> <p>8.7 Variable Time Step Methods 155</p> <p>8.8 Methods with Higher Order Truncation Error 157</p> <p>8.9 The Structure of a Simulation Program 159</p> <p>Exercises 163</p> <p><b>Part III Working with Experimental Data </b><b>165</b></p> <p><b>9 Experimental Data – Frequency Domain Analysis </b><b>167</b></p> <p>9.1 Typical Test Data 167</p> <p>9.2 Transforming to the Frequency Domain – The CFT 169</p> <p>9.3 Transforming to the Frequency Domain – The DFT 172</p> <p>9.4 Transforming to the Frequency Domain – A Faster DFT 174</p> <p>9.5 Transforming to the Frequency Domain – The FFT 175</p> <p>9.6 Transforming to the Frequency Domain – An Example 176</p> <p>9.7 Sampling and Aliasing 179</p> <p>9.8 Leakage and Windowing 184</p> <p>9.9 Decimating Data 187</p> <p>9.10 Averaging DFTs 189</p> <p>Exercises 189</p> <p><b>A Representative Dynamic Systems </b><b>193</b></p> <p>A.1 System 1 193</p> <p>A.2 System 2 193</p> <p>A.3 System 3 194</p> <p>A.4 System 4 194</p> <p>A.5 System 5 195</p> <p>A.6 System 6 195</p> <p>A.7 System 7 196</p> <p>A.8 System 8 197</p> <p>A.9 System 9 197</p> <p>A.10 System 10 198</p> <p>A.11 System 11 198</p> <p>A.12 System 12 199</p> <p>A.13 System 13 200</p> <p>A.14 System 14 200</p> <p>A.15 System 15 201</p> <p>A.16 System 16 201</p> <p>A.17 System 17 202</p> <p>A.18 System 18 202</p> <p>A.19 System 19 203</p> <p>A.20 System 20 203</p> <p>A.21 System 21 204</p> <p>A.22 System 22 204</p> <p>A.23 System 23 205</p> <p><b>B Moments and Products of Inertia </b><b>207</b></p> <p>B.1 Moments of Inertia 207</p> <p>B.2 Parallel Axis Theorem for Moments of Inertia 208</p> <p>B.3 Parallel Axis Theorem for Products of Inertia 210</p> <p>B.4 Moments of Inertia for Commonly Encountered Bodies 210</p> <p>C Dimensions and Units 213</p> <p>D Least Squares Curve Fitting 215</p> <p>Index 219</p>

<p><b>DR. RONALD J. ANDERSON</b> is a Professor in the Department of Mechanical and Materials Engineering, Queen's University at Kingston, Canada. He received his B.Sc.(Eng) from the University of Alberta in 1973, his M.Sc.(Eng) from Queen's University in 1974, and his Ph.D. from Queen's University in 1977. His doctoral research was in the field of road vehicle dynamics. From 1977 to 1979, he was a Defence Scientist with the Defence Research Establishment Atlantic where he was engaged in research on the dynamics of novel ships. From 1979 to 1981 he was Senior Dynamicist with the Urban Transportation Development Corporation where he worked on rail vehicle dynamics, particularly suspension design for steerable rail vehicles. He joined Queen's University in 1981 and, while conducting research into vehicle dynamics and multibody dynamics, has been teaching undergraduate courses on dynamics and vibrations and postgraduate courses on advanced dynamics and engineering analysis. Dr. Anderson has been the recipient of several departmental and faculty-wide teaching awards. He has also served the University in the academic administrative roles of Head of Department, Associate Dean (Research), and Dean of Graduate Studies.

<p><b>A textbook on dynamic analysis of mechanical systems, providing a unique systematic approach to enable deeper understanding of the subject</b> <p><i>The Practice of Engineering Dynamics</i> provides a systematic development of the theory and methods used for dynamic analysis of mechanical systems. Covering every essential aspect of engineering dynamics in one volume, this textbook helps readers understand how to derive the equations governing the motion of a system, use the equations to provide useful design information, and analyze experimental data measured on dynamic systems. <p>Divided into three parts—Modeling, Simulation, and Experimental Frequency Domain Analysis—the textbook's distinctive approach to the subject highlights the relationships between the topics, rather than viewing them as different fields of study. A clear, logical progression of analysis methods are applied to the governing equations: from equilibrium solutions, to analyzing the stability of equilibrium states, to frequency domain analysis, to time domain solutions. Written by a teacher and researcher with more than forty years of experience in the field, this textbook: <ul> <li>Provides comprehensive coverage of dynamic analysis of mechanical systems</li> <li>Offers a complete presentation of frequency analysis of experimental data</li> <li>Covers analysis methods rarely covered in introductory texts, such as time domain solutions</li> <li>Contains end-of-chapter exercises and numerous line drawings, figures, and tables</li> <li>Features full solutions for sample dynamic systems, animations, and supplemental resources via a companion website</li> <li>Includes an appendix of 23 mechanical systems for use in all chapter exercises</li> </ul> <p><i>The Practice of Engineering Dynamics</i> is an ideal textbook for senior undergraduate students and postgraduate students in Mechanical Engineering, as well as a valuable reference for practicing mechanical engineers in industry.

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