Dynamics : Analysis and Design of Systems in Motion Book

CHAPTER 1. BACKGROUND AND ROADMAP.

1.1 Newton’s Laws.

1.2 How You’ll Be Approaching Dynamics.

1.3 Units and Symbols.

1.4 Gravitation.

1.5 The Pieces of the Puzzle.

CHAPTER 2.  KINEMATICS OF PARTICLES.

2.1 Straight-Line Motion.

EXAMPLE 2.1 Speed Determination via Integration.

EXAMPLE 2.2 Deceleration Limit Determination.

EXAMPLE 2.3 Constant Acceleration/Speed/Distance Relation.

EXAMPLE 2.4 Position-Dependent Acceleration.

EXAMPLE 2.5 Velocity-Dependent Acceleration (A).

EXAMPLE 2.6 Velocity-Dependent Acceleration (B).

2.2 Cartesian Coordinates.

EXAMPLE 2.7 Coordinate Transformation (A).

EXAMPLE 2.8 Coordinate Transformation (B).

EXAMPLE 2.9 RectilinearTrajectory Determination (A).

EXAMPLE 2.10 RectilinearTrajectory Determination (B).

EXERCISES 2.2.

2.3 Polar and Cylindrical Coordinates.

EXAMPLE 2.11 Velocity—Polar Coordinates.

EXAMPLE 2.12 Acceleration—Polar Coordinates (A).

EXAMPLE 2.13 Acceleration—Polar Coordinates (B).

EXAMPLE 2.14 Velocity and Acceleration—Cylindrical Coordinates.

EXERCISES 2.3.

2.4 Path Coordinates.

EXAMPLE 2.15 Acceleration—Path Coordinates.

EXAMPLE 2.16 Analytical Determination of Radius of Curvature.

EXAMPLE 2.17 Speed Along a Curve.

EXERCISES 2.4.

2.5 Relative Motion and Constraints.

EXAMPLE 2.18 One Body Moving on Another.

EXAMPLE 2.19 Two Bodies Moving Independently (A).

EXAMPLE 2.20 Two Bodies Moving Independently (B).

EXAMPLE 2.21 Simple Pulley.

EXAMPLE 2.22 Double Pulley.

EXERCISES 2.5.

2.6 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA2.1 Kinematics of Variable Geometry Pulleys.

SA2.2 Multi-Axis Seat Ejection (MASE) Sled.

SA2.3 Carousel Ride.

SA2.4 Amusement Park-Style Golf Game.

CHAPTER 3. KINETICS OF PARTICLES.

3.1 Cartesian Coordinates.

EXAMPLE 3.1 Analysis of a Spaceship.

EXAMPLE 3.2 Forces Acting on an Airplane.

EXAMPLE 3.3 Response of an Underwater Probe.

EXAMPLE 3.4 Sliding Ming Bowl.

EXAMPLE 3.5 Particle in an Enclosure.

EXERCISES 3.1.

3.2 Polar Coordinates.

EXAMPLE 3.6 Forces Acting on a Payload.

EXAMPLE 3.7 Ming Bowl on a Moving Slope.

EXAMPLE 3.8 Ming Bowl on a Moving Slope with Friction.

EXAMPLE 3.9 No-Slip in a Rotating Arm.

EXERCISES 3.2.

3.3 Path Coordinates.

EXAMPLE 3.10 Forces Acting on My Car.

EXAMPLE 3.11 Finding a Rocket’s Radius of Curvature.

EXAMPLE 3.12 Determining Slip Point in aTurn.

EXAMPLE 3.13 Force and Acceleration for a Sliding Pebble.

EXERCISES 3.3.

3.4 Linear Momentum and Linear Impulse.

EXAMPLE 3.14 Changing the Space Shuttle’s Orbit.

EXAMPLE 3.15 Two-Car Collision.

3.5 Angular Momentum and Angular Impulse.

EXAMPLE 3.16 Change in Speed of a Model Plane.

EXAMPLE 3.17 Angular Momentum of a Bumper.

EXAMPLE 3.18 Angular Momentum of aTetherball.

EXERCISES 3.5.

3.6 Orbital Mechanics.

EXAMPLE 3.19 Analysis of an Elliptical Orbit.

EXAMPLE 3.20 Determining Closest Approach Distance.

EXERCISES 3.6.

3.7 Impact.

EXAMPLE 3.21 Dynamics ofTwo Pool Balls.

EXAMPLE 3.22 More Pool Ball Dynamics.

3.8 Oblique Impact.

EXAMPLE 3.23 Oblique Billiard Ball Collision.

EXAMPLE 3.24 Another Oblique Collision.

EXERCISES 3.8.

3.9 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA3.1 Escape from Colditz.

SA3.2 Kinetics of Variable Geometry Pulleys.

SA3.3 The Somatogravic Illusion.

SA3.4 The Push-Pull Maneuver.

CHAPTER 4. THE ENERGY OF PARTICLES.

4.1 Kinetic Energy.

EXAMPLE 4.1 Work to Lift a Mass.

EXAMPLE 4.2 Change in Speed Due to an Applied Force.

EXAMPLE 4.3 Change in Speed Due to Slipping.

EXERCISES 4.1.

4.2 Potential Energies and Conservative Forces.

EXAMPLE 4.4 Speed Due to a Drop.

EXAMPLE 4.5 Designing a Nutcracker.

EXAMPLE 4.6 Speed of a Particle on a Circular Hill.

EXAMPLE 4.7 Reexamination of an Orbital Problem.

EXERCISES 4.2.

4.3 Power and Ef.ciency.

EXAMPLE 4.8 Time Needed to Increase Speed.

EXAMPLE 4.9 0 to 60Time at Constant Power.

EXAMPLE 4.10 Determining a Cyclist’s Energy Efficiency.

EXERCISES 4.3.

4.4 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA4.1 Bungie Jump Energetics.

SA4.2 Escape from Colditz—TakeTwo.

CHAPTER 5.  MULTIPARTICLE SYSTEMS.

5.1 Force Balance and Linear Momentum.

EXAMPLE 5.1 Finding a Mass Center.

EXAMPLE 5.2 Finding a System’s Linear Momentum.

EXAMPLE 5.3 Motion of aTwo-Particle System.

EXAMPLE 5.4 Finding Speed of a Bicyclist/Cart.

EXAMPLE 5.5 Momentum of aThree-Mass System.

EXERCISES 5.1.

5.2 Angular Momentum.

EXAMPLE 5.6 Angular Momentum of Three Particles.

EXAMPLE 5.7 Angular Momentum About a System’s Mass Center.

EXERCISES 5.2.

5.3 Work and Energy.

EXAMPLE 5.8 Kinetic Energy of a Modi.ed Baton.

EXAMPLE 5.9 Kinetic Energy of aTranslating Modified Baton.

EXAMPLE 5.10 Spring-Mass System.

EXERCISES 5.3.

5.4 Stationary Enclosures with Mass In.ow and Out.ow.

EXAMPLE 5.11 Force Due to a Stream of Water.

EXAMPLE 5.12 Force Due to a Stream of Mass Particles

5.5 Nonconstant Mass Systems.

EXAMPLE 5.13 Motion of a Toy Rocket.

EXAMPLE 5.14 Helicopter Response to a Stream of Bullets.

EXERCISES 5.5.

5.6 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA5.1 Multi-Station Disorientation Demonstrator.

SA5.2 Sand Loader.

CHAPTER 6.  KINEMATICS OF RIGID BODIES UNDERGOING PLANAR MOTION.

6.1 Relative Velocities on a Rigid Body.

EXAMPLE 6.1 Velocity of a Pendulum.

EXAMPLE 6.2 Velocity of a Constrained Link.

EXAMPLE 6.3 Angular Speed of a Spinning Disk.

EXAMPLE 6.4 Relative Angular Velocity.

EXERCISES 6.1.

6.2 Instantaneous Center of Rotation (ICR).

EXAMPLE 6.5 Angular Speed Determination via ICR.

EXAMPLE 6.6 Velocity of the Contact Point During Roll Without Slip.

EXAMPLE 6.7 Pedaling Cadence and Bicycle Speed.

EXAMPLE 6.8 Rotation Rate of an Unwinding Reel via ICR.

EXERCISES 6.2.

6.3 Rotating Reference Frames and Rigid-Body Accelerations.

EXAMPLE 6.9 Acceleration of a Pedal Spindle for a Bicycle on Rollers.

EXAMPLE 6.10 Tip Acceleration of aTwo-Link Manipulator.

EXAMPLE 6.11 Acceleration During Roll Without  Slip.

EXAMPLE 6.12 Acceleration of a Point on a Cog of a Moving Bicycle.

EXERCISES 6.3.

6.4 Relative Motion on a Rigid Body.

EXAMPLE 6.13 Absolute Velocity of a Specimen in a Centrifuge.

EXAMPLE 6.14 Velocity Constraints—Closing Scissors.

EXAMPLE 6.15 Velocity and Acceleration in a TransportationTube.

EXAMPLE 6.16 Angular Acceleration of a Constrained Body.

EXERCISES 6.4.

6.5 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA6.1 Evaluating Head Rotation Effects.

SA6.2 Design of a Shooting Gallery Game.

SA6.3 Design of a “Snap-the-Whip” Ride.

SA6.4 Kinematics of Catapults.

CHAPTER 7.  KINETICS OF RIGID BODIES

UNDERGOINGTWO-DIMENSIONAL MOTION.

7.1 Curvilinear Translation.

EXAMPLE 7.1 Determining the Acceleration of a Translating Body.

EXAMPLE 7.2 Tension in Support Chains.

EXAMPLE 7.3 General Motion of a Swinging Sign.

EXAMPLE 7.4 Normal Forces on a Steep Hill.

EXERCISES 7.1.

7.2 Rotation About a Fixed Point.

EXAMPLE 7.5 Mass Moment of Inertia of a Rectangular Plate.

EXAMPLE 7.6 Mass Moment of Inertia of a Circular Sector.

EXAMPLE 7.7 Analysis of a Rotating Body.

EXAMPLE 7.8 Determining aWheel’s Imbalance Eccentricity.

EXAMPLE 7.9 Forces Acting at Pivot of Fireworks Display.

EXERCISES 7.2.

7.3 General Motion.

EXAMPLE 7.10 Acceleration Response of an Unrestrained Body.

EXAMPLE 7.11 Response of a Falling Rod.

EXAMPLE 7.12 Acceleration Response of a Driven Wheel.

EXAMPLE 7.13 Acceleration Response of a Driven Wheel—TakeTwo.

EXAMPLE 7.14 Tipping of a Ming Vase.

EXAMPLE 7.15 Equations of Motion for a Simple Car Model.

EXAMPLE 7.16 Analysis of a Simple Transmission.

EXERCISES 7.3.

7.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies.

EXAMPLE 7.17 Angular Impulse Applied to Space Station.

EXAMPLE 7.18 Impact Between a Pivoted Rod and a Moving Particle.

EXERCISES 7.4.

7.5 Work/Energy of Two-Dimensional Rigid Bodies.

EXAMPLE 7.19 Angular Speed of a Hinged Two-Dimensional Body.

EXAMPLE 7.20 Response of a Falling Rod via Energy.

EXAMPLE 7.21 Design of a Spring-Controlled Drawbridge.

EXERCISES 7.5.

7.6 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA7.1 Evaluation of Head Rotation Effects—TakeTwo.

SA7.2 Inertias of Catapults.

SA7.3 Catapult Launches.

SA7.4 More on Catapult Launches.

CHAPTER 8. KINEMATICSAND KINETICS OF

RIGID BODIES INTHREE-DIMENSIONAL MOTION.

8.1 Spherical Coordinates.

8.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion.

EXAMPLE 8.1 Angular Velocity of a Simplified Gyroscope.

EXAMPLE 8.2 Angular Velocity of a Hinged Plate.

8.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion.

EXAMPLE 8.3 Angular Acceleration of a Simple Gyroscope.

8.4 General Motion of and on Three-Dimensional Bodies.

EXAMPLE 8.4 Motion of a Disk Attached to a Bent Shaft.

EXAMPLE 8.5 Velocity and Acceleration of a Robotic Manipulator.

EXERCISES 8.4.

8.5 Moments and Products of Inertia for a Three-Dimensional Body.

8.6 Parallel Axis Expressions for Inertias.

EXAMPLE 8.6 Inertial Properties of a Flat Plate.

EXERCISES 8.6.

8.7 Angular Momentum.

EXAMPLE 8.7 Angular Momentum of a Flat Plate.

EXAMPLE 8.8 Angular Momentum of a Simple Structure.

EXERCISES 8.7.

8.8 Equations of Motion for a Three-Dimensional Body.

EXAMPLE 8.9 Reaction Forces of a Constrained, Rotating Body.

EXERCISES 8.8.

8.9 Energy of Three-Dimensional Bodies.

EXAMPLE 8.10 Kinetic Energy of a Rotating Disk.

EXERCISES 8.9.

8.10 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA8.1 Evaluating Head Rotation Effects.

CHAPTER 9. VIBRATORY MOTIONS.

9.1 Undamped, Free Response for Single-Degree-of-Freedom Systems.

EXAMPLE 9.1 Displacement Response of a Single-Story Building.

EXAMPLE 9.2 Natural Frequency of a Cantilevered Balcony.

EXERCISES 9.1.

9.2 Undamped, Sinusoidally Forced Response for Single-Degree-of-Freedom Systems.

EXAMPLE 9.3 Forced Response of a Spring-Mass System.

EXAMPLE 9.4 Time Response of an Undamped System.

EXERCISES 9.2.

9.3 Damped, Free Response for

Single-Degree-of-Freedom Systems.

EXAMPLE 9.5 Vibration Response of a Golf Club.

EXERCISES 9.3.

9.4 Damped, Sinusoidally Forced Response for

Single-Degree-of-Freedom Systems.

EXAMPLE 9.6 Response of a Sinusoidally Forced,

Spring-Mass Damper.

EXAMPLE 9.7 Response of a Simple Car Model

on a Wavy Road.

EXERCISES 9.4.

9.5 Just the Facts.

SYSTEM ANALYSIS (SA) EXERCISES.

SA9.1 Clothes Washer Vibrations.

APPENDIX A:  NUMERICAL INTEGRATION LIGHT.

APPENDIX B:  PROPERTIES OF PLANEAND SOLID BODIES.

APPENDIX C:  SOME USEFUL MATHEMATICAL FACTS.

APPENDIX D:  MATERIAL DENSITIES.

BIBLIOGRAPHY.

INDEX.