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Table of Contents
1 Cover
2 Preface
4 Part I: Modeling: Deriving Equations of Motion 1 Kinematics 1.1 Derivatives of Vectors 1.2 Performing Kinematic Analysis 1.3 Two Dimensional Motion with Constant Length 1.4 Two Dimensional Motion with Variable Length 1.5 Three Dimensional Kinematics 1.6 Absolute Angular Velocity and Acceleration 1.7 The General Acceleration Expression 2 Newton's Equations of Motion 2.1 The Study of Motion 2.2 Newton's Laws 2.3 Newton's Second Law for a Particle 2.4 Deriving Equations of Motion for Particles 2.5 Working with Rigid Bodies 2.6 Using in the Rigid Body Force Balance 2.7 Using in the Rigid Body Force Balance 2.8 Moment Balance for a Rigid Body 2.9 The Angular Momentum Vector – 2.10 A Physical Interpretation of Moments and Products of Inertia 2.11 Euler's Moment Equations 2.12 Throwing a Spiral 2.13 A Two Body System 2.14 Gyroscopic Motion 3 Lagrange's Equations of Motion 3.1 An Example to Start 3.2 Lagrange's Equation for a Single Particle 3.3 Generalized Forces 3.4 Generalized Forces as Derivatives of Potential Energy 3.5 Dampers – Rayleigh's Dissipation Function 3.6 Kinetic Energy of a Free Rigid Body 3.7 A Two Dimensional Example using Lagrange's Equation 3.8 Standard Form of the Equations of Motion
5 Part II: Simulation: Using the Equations of Motion 4 Equilibrium Solutions 4.1 The Simple Pendulum 4.2 Equilibrium with Two Degrees of Freedom 4.3 Equilibrium with Steady Motion 4.4 The General Equilibrium Solution 5 Stability 5.1 Analytical Stability 5.2 Linearization of Functions 5.3 Example: A System with Two Degrees of Freedom 5.4 Routh Stability Criterion 5.5 Standard Procedure for Stability Analysis 6 Mode Shapes 6.1 Eigenvectors 6.2 Comparing Translational and Rotational Degrees of Freedom 6.3 Nodal Points in Mode Shapes 6.4 Mode Shapes with Damping 6.5 Modal Damping 7 Frequency Domain Analysis 7.1 Modeling Frequency Response 7.2 Seismic Disturbances 7.3 Power Spectral Density 8 Time Domain Solutions 8.1 Getting the Equations of Motion Ready for Time Domain Simulation 8.2 A Time Domain Example 8.3 Numerical Schemes for Solving the Equations of Motion 8.4 Euler Integration 8.5 An Example Using the Euler Integrator 8.6 The Central Difference Method: An Method 8.7 Variable Time Step Methods 8.8 Methods with Higher Order Truncation Error 8.9 The Structure of a Simulation Program
6 Part III: Working with Experimental Data 9 Experimental Data – Frequency Domain Analysis
