Preface |
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xv | |
Authors |
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xix | |
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1 Introduction and Fundamentals |
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1 | (6) |
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1 | (1) |
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1.2 Short History of Dynamics |
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1 | (2) |
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3 | (4) |
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2 Planar Kinematics of Particles |
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7 | (38) |
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7 | (1) |
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2.2 Motion in a Straight Line |
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7 | (3) |
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10 | (1) |
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2.3 Particle Motion in a Plane: Cartesian Coordinates |
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10 | (2) |
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2.4 Coordinate Transformations: Relationships between Components of a Vector in Two-Coordinate Systems |
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12 | (2) |
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2.5 Particle Motion in a Plane: Polar Coordinates |
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14 | (3) |
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2.6 Particle Motion in a Plane: Normal-Tangential (Path) Coordinates |
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17 | (3) |
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2.7 Moving between Cartesian, Polar- and Path-Coordinate Definitions for Velocity and Acceleration Components |
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20 | (7) |
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2.7.1 Example That Is Naturally Analyzed with Cartesian Components |
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20 | (3) |
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2.7.2 Example That Is Naturally Analyzed Using Polar Coordinates |
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23 | (2) |
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2.7.3 Example That Is Naturally Analyzed with Path-Coordinate Components |
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25 | (2) |
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2.8 Time-Derivative Relationships in Two-Coordinate Systems |
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27 | (2) |
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2.9 Velocity and Acceleration Relationships in Two Cartesian Coordinate Systems |
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29 | (4) |
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2.9.1 Comparisons to Polar-Coordinate Definitions |
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30 | (1) |
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2.9.2 Coordinate System Expressions for Kinematic Equations |
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31 | (1) |
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2.9.3 Coordinate System Observers |
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31 | (2) |
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2.10 Relative Position, Velocity, and Acceleration Vectors between Two Points in the Same Coordinate System |
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33 | (3) |
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2.11 Summary and Discussion |
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36 | (9) |
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38 | (7) |
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3 Planar Kinetics of Particles |
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45 | (120) |
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45 | (2) |
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3.2 Differential Equations of Motion for a Particle Moving in a Straight Line: An Introduction to Physical Modeling |
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47 | (36) |
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3.2.1 Constant Acceleration: Free Fall of a Particle without Drag |
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47 | (2) |
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3.2.2 Acceleration as a Function of Displacement: Spring Forces |
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49 | (1) |
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3.2.2.1 Deriving the Equation of Motion Starting with the Spring Undeflected |
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49 | (1) |
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3.2.2.2 Deriving the Equation of Motion for Motion about Equilibrium |
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50 | (2) |
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3.2.2.3 Developing a Time Solution for the Equation of Motion |
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52 | (1) |
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3.2.2.4 Developing a Solution for Y as a Function of Y |
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53 | (1) |
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3.2.2.5 Negative Sign for the Stiffness Coefficient |
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54 | (1) |
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3.2.3 Energy Dissipation: Viscous Damping |
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54 | (1) |
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54 | (1) |
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3.2.3.2 Deriving the Equation of Motion for a Mass--Spring--Damper System |
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55 | (1) |
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3.2.3.3 Motion about the Equilibrium Position |
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55 | (1) |
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3.2.3.4 Developing a Time Solution for the Equation of Motion |
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55 | (5) |
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3.2.3.5 Characterizing Damping |
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60 | (1) |
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3.2.3.6 Solution for Y as a Function of Y Including Damping? |
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61 | (1) |
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3.2.3.7 Negative Damping and Dynamic Instability |
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62 | (1) |
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3.2.4 Base Excitation for a Spring--Mass--Damper System |
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62 | (1) |
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3.2.4.1 Deriving the Equation of Motion |
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62 | (5) |
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3.2.4.2 Relative Motion due to Base Excitation |
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67 | (1) |
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3.2.5 Harmonic Excitation for a 1DOF, Spring--Mass--Damper System: Solution for Motion in the Frequency Domain |
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67 | (4) |
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71 | (2) |
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3.2.5.2 Steady-State Relative Motion due to Base Excitation |
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73 | (1) |
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3.2.5.3 Rotating-Imbalance Excitation |
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74 | (3) |
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3.2.5.4 Summary and Extensions |
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77 | (1) |
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3.2.6 Energy Dissipation: Coulomb Damping |
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78 | (2) |
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3.2.7 Quadratic Damping: Aerodynamic Drag |
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80 | (1) |
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3.2.7.1 Terminal Velocity Calculation |
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80 | (3) |
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83 | (1) |
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3.3 More Motion in a Straight Line: Degrees of Freedom and Equations of Kinematic Constraints |
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83 | (9) |
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3.3.1 Pulleys: Equations of Motion and Equations of Constraint |
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84 | (5) |
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3.3.2 Linkage Problems: More Equations of Constraint |
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89 | (3) |
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3.4 Motion in a Plane: Equations of Motion and Forces of Constraint |
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92 | (13) |
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3.4.1 Cartesian Coordinate Applications: Trajectory Motion in a Vertical Plane |
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92 | (1) |
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92 | (3) |
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3.4.1.2 Trajectory Motion with Aerodynamic Drag |
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95 | (1) |
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3.4.1.3 Trajectory Motion and Coulomb Drag |
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96 | (1) |
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3.4.2 Polar-Coordinate Applications |
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96 | (1) |
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3.4.2.1 Particle Sliding on the Inside of a Horizontal Cylinder without Friction |
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96 | (1) |
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3.4.2.2 Particle Sliding on the Inside of a Horizontal Cylinder with Coulomb Friction |
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97 | (1) |
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98 | (2) |
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3.4.2.4 Simple Pendulum with Damping |
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100 | (2) |
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3.4.3 Path-Coordinate Applications |
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102 | (2) |
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3.4.4 Summary and Overview |
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104 | (1) |
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3.5 Particle Kinetics Examples with More than 1DOF |
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105 | (20) |
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3.5.1 Developing Equations of Motion for Problems Having More than 1DOF |
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105 | (1) |
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3.5.1.1 Developing Equations of Motion for a Two-Mass Vibration Example |
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105 | (5) |
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3.5.1.2 Developing Equations of Motion for a Double Pendulum |
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110 | (2) |
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3.5.2 Analyzing Multidegree-of-Freedom Vibration Problems |
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112 | (1) |
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3.5.2.1 Analyzing Undamped 2DOF Vibration Problems |
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112 | (5) |
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3.5.2.2 Free Motion from Initial Conditions (the Homogeneous Solution) |
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117 | (3) |
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3.5.2.3 Modal Damping Models |
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120 | (2) |
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3.5.2.4 Steady-State Solutions due to Harmonic Excitation |
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122 | (2) |
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3.5.2.5 Harmonic Response with Damping |
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124 | (1) |
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3.6 Work--Energy Applications for 1DOF Problems in Plane Motion |
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125 | (11) |
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3.6.1 Work---Energy Equation and Its Application |
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126 | (2) |
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3.6.1.1 More on Spring Forces and Spring Potential-Energy Functions |
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128 | (2) |
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3.6.1.2 More on the Force of Gravity and the Potential-Energy Function for Gravity |
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130 | (2) |
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3.6.2 Deriving Equations of Motion from Work--Energy Relations |
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132 | (4) |
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3.7 Linear-Momentum Applications in Plane Motion |
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136 | (6) |
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3.7.1 Collision Problems in One Dimension |
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137 | (1) |
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3.7.2 Coefficient of Restitution |
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138 | (1) |
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3.7.3 Collision Problems in Two Dimensions |
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139 | (3) |
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142 | (2) |
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3.8.1 Developing the Moment-of-Momentum Equation for a Particle |
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142 | (1) |
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3.8.2 Applying Conservation of Moment of Momentum for a Particle |
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143 | (1) |
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3.8.2.1 Two Particles Connected by an Inextensible Cord |
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143 | (1) |
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144 | (1) |
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3.9 Summary and Discussion |
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144 | (21) |
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146 | (19) |
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4 Planar Kinematics of Rigid Bodies |
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165 | (42) |
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165 | (1) |
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4.2 Rotation about a Fixed Axis |
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165 | (2) |
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4.3 Velocity and Acceleration Relationships for Two Points in a Rigid Body |
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167 | (4) |
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4.4 Rolling without Slipping |
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171 | (7) |
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171 | (1) |
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4.4.1.1 Geometric Development |
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171 | (2) |
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4.4.1.2 Vector Developments of Velocity Relationships |
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173 | (1) |
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4.4.1.3 Vector Developments of Acceleration Results |
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174 | (4) |
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4.4.2 Wheel Rolling inside or on a Cylindrical Surface |
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178 | (1) |
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4.4.2.1 Wheel Rolling inside a Cylindrical Surface |
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178 | (1) |
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4.4.2.2 Wheel Rolling on the Outside of a Cylindrical Surface |
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178 | (1) |
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178 | (16) |
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178 | (1) |
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4.5.2 Slider-Crank Mechanism |
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179 | (1) |
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4.5.2.1 Geometric Approach |
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179 | (2) |
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4.5.2.2 Vector Approach for Velocity and Acceleration Results |
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181 | (1) |
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4.5.3 Four-Bar-Linkage Example |
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182 | (1) |
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4.5.3.1 Geometric Approach |
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183 | (2) |
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4.5.3.2 Vector Approach for Velocity and Acceleration Relationships |
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185 | (3) |
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4.5.4 Another Slider-Crank Mechanism |
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188 | (1) |
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4.5.4.1 Geometric Approach |
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188 | (2) |
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4.5.4.2 Vector, Two-Coordinate System Approach for Velocity and Acceleration Relationships |
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190 | (2) |
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4.5.4.3 Solution for the Velocity and Acceleration of Point D |
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192 | (1) |
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193 | (1) |
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4.6 Summary and Discussion |
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194 | (13) |
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194 | (13) |
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5 Planar Kinetics of Rigid Bodies |
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207 | (132) |
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207 | (1) |
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5.2 Inertia Properties and the Parallel-Axis Formula |
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207 | (4) |
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5.2.1 Centroids and Moments of Inertia |
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207 | (2) |
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5.2.2 Parallel-Axis Formula |
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209 | (2) |
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5.3 Governing Force and Moment Equations for a Rigid Body |
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211 | (4) |
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212 | (1) |
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213 | (2) |
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5.3.2.1 Reduced Forms for the Moment Equation |
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215 | (1) |
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5.4 Kinetic Energy for Planar Motion of a Rigid Body |
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215 | (1) |
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5.5 Fixed-Axis-Rotation Applications of the Force, Moment, and Energy Equations |
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216 | (8) |
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5.5.1 Rotor in Frictionless Bearings: Moment Equation |
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216 | (1) |
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5.5.2 Rotor in Frictionless Bearings: Energy Equation |
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217 | (1) |
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5.5.3 Rotor in Bearings with Viscous Drag: Moment Equation |
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217 | (1) |
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5.5.4 Rotor in Bearings with Viscous Drag: Energy Equation |
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218 | (1) |
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5.5.5 Torsional Vibration Example: Moment Equation |
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218 | (1) |
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5.5.6 Torsional Vibration Example: Energy Equation |
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219 | (1) |
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5.5.7 Pulley/Weight Example: Free-Body Approach |
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220 | (1) |
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5.5.8 Pulley/Weight Example: Energy Approach |
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221 | (1) |
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5.5.9 Example Involving a Disk and a Particle: Newtonian Approach |
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221 | (1) |
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5.5.10 Example Involving a Disk and a Particle: Work--Energy Approach |
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222 | (1) |
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5.5.11 Two Driven Pulleys Connected by a Belt |
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223 | (1) |
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5.5.12 Two Driven Pulleys Connected by a Belt: Work-Energy Approach |
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224 | (1) |
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5.6 Compound Pendulum Applications |
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224 | (15) |
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5.6.1 Simple Compound Pendulum: EOM, Linearization, and Stability |
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224 | (5) |
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5.6.2 Compound Pendulum with Damping |
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229 | (1) |
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5.6.3 Compound Pendulum/Spring and Damper Connections: Linearization and Equilibrium |
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230 | (1) |
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5.6.3.1 Compound Pendulum with a Spring Attachment to Ground: Moment Equation |
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230 | (1) |
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5.6.3.2 Compound Pendulum with a Spring Attachment to Ground: Energy Approach |
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231 | (1) |
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5.6.3.3 Compound Pendulum with a Damper Attachment to Ground: Moment Equation |
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232 | (2) |
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5.6.3.4 Bars Supported by Springs: Preload and Equilibrium |
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234 | (3) |
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5.6.3.5 Closing Comments and (Free) Advice |
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237 | (1) |
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5.6.4 Prescribed Acceleration of a Compound Pendulum's Pivot Support Point |
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238 | (1) |
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5.7 General Applications of Force, Moment, and Energy Equations for Planar Motion of a Rigid Body |
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239 | (54) |
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5.7.1 Rolling-without-Slipping Examples: Newtonian and Energy Approaches |
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240 | (1) |
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5.7.1.1 Cylinder Rolling Down an Inclined Plane: Free-Body-Diagram Approach |
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240 | (2) |
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5.7.1.2 Cylinder Rolling Down an Inclined Plane: Work-Energy Approach |
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242 | (1) |
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5.7.1.3 Imbalanced Cylinder Rolling Down an Inclined Plane: Newtonian Approach |
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242 | (2) |
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5.7.1.4 Imbalanced Cylinder Rolling Down an Inclined Plane: Work--Energy Approach |
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244 | (1) |
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5.7.1.5 Half Cylinder Rolling on a Horizontal Plane: Newtonian Approach |
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244 | (2) |
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5.7.1.6 Half-Cylinder Rotating on a Horizontal Plane: Energy Approach |
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246 | (1) |
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5.7.1.7 Cylinder, Restrained by a Spring and Rolling on a Plane: Newtonian Approach |
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247 | (1) |
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5.7.1.8 Cylinder, Restrained by a Spring and Rolling on a Plane: Energy Approach |
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248 | (1) |
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5.7.1.9 Cylinder Rolling inside a Cylindrical Surface |
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248 | (2) |
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5.7.1.10 Pulley-Assembly Example: Newtonian Approach |
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250 | (1) |
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5.7.1.11 Pulley-Assembly Example: Energy Approach |
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251 | (1) |
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5.7.1.12 Closing Comments |
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251 | (1) |
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5.7.2 One Degree of Freedom, Planar-Motion Applications, and Newtonian and Energy Approaches |
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252 | (1) |
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5.7.2.1 Uniform Bar, Acted on by an External Force, Moving in Slots, and Constrained by Springs |
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252 | (3) |
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5.7.2.2 Adding Viscous Damping to the Slots Supporting the Uniform Bar |
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255 | (1) |
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5.7.2.3 Bar Leaning and Sliding on a Smooth Floor and against a Smooth Vertical Wall |
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256 | (2) |
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5.7.2.4 Bar Leaning and Sliding on a Floor and against a Vertical Wall with Coulomb Friction |
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258 | (2) |
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5.7.2.5 Summary and Discussion |
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260 | (1) |
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5.7.3 Multibody, Single-Coordinate Applications of the Work--Energy Equation |
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260 | (1) |
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5.7.3.1 Two Bars with an Applied Force and a Connecting Spring |
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260 | (3) |
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5.7.3.2 Hinged Bar/Plate Example |
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263 | (1) |
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5.7.3.3 Parallel, Double-Bar Arrangement for Retracting a Cylinder |
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264 | (1) |
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265 | (1) |
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5.7.4 Examples Having More than One Degree of Freedom |
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266 | (1) |
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5.7.4.1 Torsional Vibration Examples |
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266 | (3) |
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5.7.4.2 Beams as Springs: Bending Vibration Examples |
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269 | (8) |
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5.7.4.3 Jeffcott/Laval Rotor Model |
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277 | (2) |
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5.7.4.4 Translating Mass with an Attached Compound Pendulum |
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279 | (1) |
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5.7.4.5 Swinging Bar Supported at Its End by a Cord |
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280 | (3) |
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5.7.4.6 Double Compound Pendulum |
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283 | (1) |
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284 | (1) |
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5.7.5.1 Slider-Crank Mechanism |
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284 | (4) |
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5.7.5.2 Four-Bar-Linkage Example |
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288 | (3) |
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5.7.5.3 Alternative Slider-Crank Mechanism |
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291 | (1) |
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292 | (1) |
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5.8 Moment of Momentum for Planar Motion |
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293 | (9) |
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5.8.1 Developing Moment-of-Momentum Equations for Planar Motion of Rigid Bodies |
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293 | (3) |
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5.8.2 Applying Moment-of-Momentum Equations in Planar Dynamics |
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296 | (1) |
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5.8.2.1 Two Spinning Wheels Connected by an Adjustable-Tension Belt |
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296 | (2) |
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5.8.2.2 Particle of Mass Impacting with a Compound Pendulum |
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298 | (1) |
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5.8.2.3 Spinning Baton Striking the Ground |
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299 | (2) |
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5.8.2.4 Rolling Cylinder That Encounters an Inclined Plane |
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301 | (1) |
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5.9 Summary and Discussion |
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302 | (37) |
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304 | (35) |
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6 Lagrange's Equations of Motion |
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339 | (30) |
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339 | (1) |
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6.2 Deriving Lagrange's Equations of Motion |
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339 | (3) |
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6.3 Applying Lagrange's Equation of Motion to Problems without Kinematic Constraints |
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342 | (7) |
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6.3.1 Two-Mass Vibration Example |
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342 | (1) |
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6.3.2 Double Pendulum Example |
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343 | (1) |
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6.3.3 Coupled Cart--Pendulum |
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344 | (2) |
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6.3.4 Cart--Pendulum Example with an Additional External Force |
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346 | (1) |
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6.3.5 Cart--Pendulum Example with Viscous Dissipation Forces |
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346 | (1) |
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6.3.6 Cart--Pendulum Example with a Coulomb-Friction Moment in the Pendulum Support Pivot |
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347 | (1) |
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348 | (1) |
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6.4 Conservation of Momenta from Lagrange's Equations of Motion |
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349 | (3) |
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6.4.1 Two Particles Connected by an Inextensible Cord |
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349 | (1) |
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6.4.2 Particle Moving on the Inner Surface of an Inverted Cone |
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350 | (1) |
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6.4.3 Two Translating Masses Connected by a Linear Spring |
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351 | (1) |
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352 | (1) |
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6.5 Application of Lagrange's Equations to Examples with Algebraic Kinematic Constraints |
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352 | (8) |
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6.5.1 Accounting for Algebraic Constraints with Lagrange Multipliers |
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353 | (1) |
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6.5.1.1 Simple Pendulum as an Example with a Kinematic Constraint |
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354 | (1) |
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6.5.1.2 Two-Bar Linkage Problem with a Nonlinear Kinematic Constraint |
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354 | (2) |
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6.5.1.3 Bar Supported by a Wire and a Horizontal Plane |
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356 | (2) |
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6.5.2 Lagrange Multipliers for Multiple Algebraic Constraints |
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358 | (1) |
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6.5.2.1 Three-Bar Linkage Example |
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358 | (2) |
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360 | (1) |
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6.6 Using Lagrange Multipliers to Define Reaction Forces for Systems with Generalized Coordinates |
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360 | (3) |
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6.6.1 Finding the Tension in the Cord of a Simple Pendulum |
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361 | (1) |
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6.6.2 Uniform Bar Leaning and Sliding on a Floor and against a Vertical Wall |
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361 | (2) |
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6.7 Summary and Discussion |
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363 | (6) |
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364 | (5) |
Appendix A Essentials of Matrix Algebra |
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369 | (2) |
Appendix B Essentials of Differential Equations |
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371 | (8) |
Appendix C Mass Properties of Common Solid Bodies |
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379 | (4) |
Appendix D Answers to Selected Problems |
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383 | (64) |
References |
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447 | (2) |
Index |
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449 | |