7 A Representative Dynamic Systems A.1 System 1 A.2 System 2 A.3 System 3 A.4 System 4 A.5 System 5 A.6 System 6 A.7 System 7 A.8 System 8 A.9 System 9 A.10 System 10 A.11 System 11 A.12 System 12 A.13 System 13 A.14 System 14 A.15 System 15 A.16 System 16 A.17 System 17 A.18 System 18 A.19 System 19 A.20 System 20 A.21 System 21 A.22 System 22 A.23 System 23
8 B Moments and Products of Inertia B.1 Moments of Inertia B.2 Parallel Axis Theorem for Moments of Inertia B.3 Parallel Axis Theorem for Products of Inertia B.4 Moments of Inertia for Commonly Encountered Bodies
10 D Least Squares Curve Fitting
11 Index
List of Tables
1 Chapter 5Table 5.1 Parameter values for the two degree of freedom example.Table 5.2 Eigenvalues and eigenvectors for the two degree of freedom example.Table 5.3 The Routh table.Table 5.4 The initial Routh table for the two degrees of freedom example.Table 5.5 The final Routh table for the two degrees of freedom example.
2 Chapter 6Table 6.1 Parameters for the rigid rod example.
3 Chapter 7Table 7.1 Parameters for the linear system with two masses.
4 Chapter 8Table 8.1 Euler integration example.Table 8.2 Pendulum simulation pseudo‐code.Table 8.3 General simulation pseudo‐code.
5 Chapter 9Table 9.1 Fourier transforms computational effort.Table 9.2 Sampled data.Table 9.3 DFT coefficients.Table 9.4 DFT coefficients.
6 4Table D.1 Sample data points.
List of Illustrations
1 Chapter 1Figure 1.1 A vector changing with time.Figure 1.2 Even 2D problems are 3D.Figure 1.3 A rigid rod rotating about a fixed point.Figure 1.4 A slider in a slot.Figure 1.5 A three dimensional robot.Figure 1.6 Relative position vectors.Figure 1.7 The velocity and acceleration components of the slider.
2 Chapter 2Figure 2.1 A slider in a slot.Figure 2.2 Creating the Free Body Diagram of the slider.Figure 2.3 A single particle in a rigid body.Figure 2.4 Free body diagram of a single particle in a rigid body.Figure 2.5 A single mass system to help interpret inertia properties.Figure 2.6 Term 1 – a product of inertia term.Figure 2.7 Term 2 – a product of inertia term.Figure 2.8 Term 3 – a moment of inertia term.Figure 2.9 An American football in flight.Figure 2.10 A cylinder on a wedge.Figure 2.11 FBDs of the cylinder and the wedge.Figure 2.12 A spinning top.Figure 2.13 A bicycle.Figure 2.14 The “tipped” top.Figure 2.15 The bicycle turning to the right.
3 Chapter 3Figure 3.1 A mass on a wire.Figure 3.2 Gravitational force acting on a mass.Figure 3.3 Spring force acting on a mass.Figure 3.4 A linear viscous damper.Figure 3.5 A single particle in a rigid body.Figure 3.6 2D rigid body example.Figure 3.7 2D rigid body potential energy.
4 Chapter 4Figure 4.1 A simple pendulum.Figure 4.2 The equilibrium solutions for the 2D example.Figure 4.3 An eccentric rotating body.Figure 4.4 The constant acceleration case.
5 Chapter 5Figure 5.1 Stability response types.Figure 5.2 Linearization.
6 Chapter 6Figure 6.1 The higher frequency mode for the two degrees of freedom system (...Figure 6.2 The lower frequency mode for the two degrees of freedom system (0...Figure 6.3 A rigid rod supported on springs.Figure 6.4 Undamped mode shapes for the rigid rod supported on springs.Figure 6.5 Nodal points.Figure 6.6 Damped mode shapes for the rigid rod supported on springs.Figure 6.7 Calculating the damping ratio from the location of an eigenvalue....Figure 6.8 Waveforms for different percent damping.
7 Chapter 7Figure 7.1 A linear system with two masses.Figure 7.2 Amplitude response of mass 1.Figure 7.3 Phase