Benson H. Tongue, Ph.D., is a Professor of Mechanical Engineering at University of California-Berkeley. He received his Ph.D. from Princeton University in 1988, and currently teaches graduate and undergraduate courses in dynamics, vibrations, and control theory.Dr. Tongue has served as Associate Technical Editor of the ASME Journal of Vibration and Acoustics as a member of the ASME Committee on Dynamics of Structures and Systems. He is the recipient of the NSF Presidential Young Investigator Award, the Sigma Xi Junior Faculty award, and the Pi Tau Sigma Excellence in Teaching award. He serves as a reviewer for numerous journals and funding agencies and is the author of more than eighty publications.Sheri D. Sheppard Ph.D., is the Carnegie Foundation for the Advancement of Teaching Senior Scholar principally responsible for the Preparations for the Professions Program (PPP) engineering study. She is an Associate Professor of Mechanical Engineering at Stanford University. She received her Ph.D. from the University of Michigan in 1985.Dr. Sheppard was recently named co-principal investigator on a NSF grant to form the Deter for the Advancement of Engineering Education (CAEE). In 1999, she was named a fellow of the American Society of Mechanical Engineering (ASME) and the American Association for the Advancement of Science (AAAS). In 2004 Dr. Shepard was awarded the ASEE Chester F. Carlson Award in recognition of distinguished accomplishments in engineering education.

• Chapter 1Background and Roadmap 11.1 Newton’s Laws 21.2 How You’ll Be Approaching Dynamics 21.3 Units and Symbols 61.4 Gravitation 101.5 The Pieces of the Puzzle 11Chapter 2Motion of Translating Bodies 162.1 Straight-Line Motion 17Examples 23Exercises 2.1 282.2 Cartesian Coordinates 33Examples 38Exercises 2.2 432.3 Polar and Cylindrical Coordinates 47Examples 54Exercises 2.3 582.4 Path Coordinates 64Examples 67Exercises 2.4 712.5 Relative Motion and Constraints 76Examples 82Exercises 2.5 872.6 Just the Facts 93System Analysis 97Chapter 3Inertial Response of Translating Bodies 993.1 Cartesian Coordinates 100Examples 102Exercises 3.1 1083.2 Polar Coordinates 119Examples 120Exercises 3.2 1273.3 Path Coordinates 133Examples 134Exercises 3.3 1393.4 Linear Momentum and Linear Impulse 143Examples 145Exercises 3.4 1473.5 Angular Momentum and Angular Impulse 155Examples 158Exercises 3.5 1613.6 Orbital Mechanics 163Examples 176Exercises 3.6 1783.7 Impact 183Examples 189Exercises 3.7 1913.8 Oblique Impact 193Examples 196Exercises 3.8 2003.9 Just the Facts 203System Analysis 206Chapter 4Energetics of Translating Bodies 2094.1 Kinetic Energy 210Examples 212Exercises 4.1 2154.2 Potential Energies and Conservative Forces 220Examples 225Exercises 4.2 2314.3 Power and Efficiency 243Examples 247Exercises 4.3 2504.4 Just the Facts 255System Analysis 257Chapter 5Multibody Systems 2585.1 Force Balance and Linear Momentum 259Examples 263Exercises 5.1 2685.2 Angular Momentum 273Examples 277Exercises 5.2 2795.3 Work and Energy 282Examples 284Exercises 5.3 2875.4 Stationary Enclosures with Mass Inflow and Outflow 288Examples 291Exercises 5.4 2935.5 Nonconstant Mass Systems 299Examples 303Exercises 5.5 3055.6 Just the Facts 310System Analysis 313Chapter 6Kinematics of Rigid Bodies Undergoing Planar Motion 3146.1 Relative Velocities on a Rigid Body 315Examples 320Exercises 6.1 3256.2 Instantaneous Center of Rotation (icr) 333Examples 335Exercises 6.2 3416.3 Rotating Reference Frames and Rigid-Body Accelerations 346Examples 350Exercises 6.3 3566.4 Relative Motion on a Rigid Body 361Examples 365Exercises 6.4 3716.5 Just the Facts 378System Analysis 380Chapter 7Kinetics of Rigid Bodies Undergoing Two-dimensional Motion 3827.1 Curvilinear Translation 384Examples 385Exercises 7.1 3927.2 Rotation about a Fixed Point 396Examples 401Exercises 7.2 4117.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 457Examples 460Exercises 7.4 4627.5 Work/Energy of Two-Dimensional Rigid Bodies 468Examples 471Exercises 7.5 4757.6 Just the Facts 482System Analysis 484Chapter 8Kinematics and Kinetics of Rigid Bodies in Three-dimensional Motion 4878.1 Spherical Coordinates 4888.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 489Examples 4938.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 495Examples 4968.4 General Motion of and on Three-Dimensional Bodies 497Examples 498Exercises 8.4 5028.5 Moments and Products of Inertia for a Three-Dimensional Body 5068.6 Parallel Axis Expressions for Inertias 508Examples 510Exercises 8.6 5118.7 Angular Momentum 513Examples 517Exercises 8.7 5208.8 Equations of Motion for a Three-Dimensional Body 521Examples 524Exercises 8.8 5268.9 Energy of Three-Dimensional Bodies 532Examples 534Exercises 8.9 5368.10 Just the Facts 537System Analysis 5417.3 General Motion 422Examples 425Exercises 7.3 444Chapter 9Vibratory Motions 5429.1 Undamped, Free Response for Single-Degree-of-Freedom Systems 543Examples 546Exercises 9.1 5499.2 Undamped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 555Examples 558Exercises 9.2 5609.3 Damped, Free Response for Single-Degree-of-Freedom Systems 563Examples 567Exercises 9.3 5689.4 Damped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 569Examples 572Exercises 9.4 5759.5 Just the Facts 576System Analysis 579Appendix ANumerical Integration Light 580Appendix BProperties of Plane and Solid Bodies 588Appendix CSome Useful Mathematical Facts 592Appendix DMaterial Densities 595Bibliography 597Index 598

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Benson H. Tongue, Ph.D., is a Professor of Mechanical Engineering at University of California-Berkeley. He received his Ph.D. from Princeton University in 1988, and currently teaches graduate and undergraduate courses in dynamics, vibrations, and control theory.Dr. Tongue has served as Associate Technical Editor of the ASME Journal of Vibration and Acoustics as a member of the ASME Committee on Dynamics of Structures and Systems. He is the recipient of the NSF Presidential Young Investigator Award, the Sigma Xi Junior Faculty award, and the Pi Tau Sigma Excellence in Teaching award. He serves as a reviewer for numerous journals and funding agencies and is the author of more than eighty publications.Sheri D. Sheppard Ph.D., is the Carnegie Foundation for the Advancement of Teaching Senior Scholar principally responsible for the Preparations for the Professions Program (PPP) engineering study. She is an Associate Professor of Mechanical Engineering at Stanford University. She received her Ph.D. from the University of Michigan in 1985.Dr. Sheppard was recently named co-principal investigator on a NSF grant to form the Deter for the Advancement of Engineering Education (CAEE). In 1999, she was named a fellow of the American Society of Mechanical Engineering (ASME) and the American Association for the Advancement of Science (AAAS). In 2004 Dr. Shepard was awarded the ASEE Chester F. Carlson Award in recognition of distinguished accomplishments in engineering education.

• Chapter 1Background and Roadmap 11.1 Newton’s Laws 21.2 How You’ll Be Approaching Dynamics 21.3 Units and Symbols 61.4 Gravitation 101.5 The Pieces of the Puzzle 11Chapter 2Motion of Translating Bodies 162.1 Straight-Line Motion 17Examples 23Exercises 2.1 282.2 Cartesian Coordinates 33Examples 38Exercises 2.2 432.3 Polar and Cylindrical Coordinates 47Examples 54Exercises 2.3 582.4 Path Coordinates 64Examples 67Exercises 2.4 712.5 Relative Motion and Constraints 76Examples 82Exercises 2.5 872.6 Just the Facts 93System Analysis 97Chapter 3Inertial Response of Translating Bodies 993.1 Cartesian Coordinates 100Examples 102Exercises 3.1 1083.2 Polar Coordinates 119Examples 120Exercises 3.2 1273.3 Path Coordinates 133Examples 134Exercises 3.3 1393.4 Linear Momentum and Linear Impulse 143Examples 145Exercises 3.4 1473.5 Angular Momentum and Angular Impulse 155Examples 158Exercises 3.5 1613.6 Orbital Mechanics 163Examples 176Exercises 3.6 1783.7 Impact 183Examples 189Exercises 3.7 1913.8 Oblique Impact 193Examples 196Exercises 3.8 2003.9 Just the Facts 203System Analysis 206Chapter 4Energetics of Translating Bodies 2094.1 Kinetic Energy 210Examples 212Exercises 4.1 2154.2 Potential Energies and Conservative Forces 220Examples 225Exercises 4.2 2314.3 Power and Efficiency 243Examples 247Exercises 4.3 2504.4 Just the Facts 255System Analysis 257Chapter 5Multibody Systems 2585.1 Force Balance and Linear Momentum 259Examples 263Exercises 5.1 2685.2 Angular Momentum 273Examples 277Exercises 5.2 2795.3 Work and Energy 282Examples 284Exercises 5.3 2875.4 Stationary Enclosures with Mass Inflow and Outflow 288Examples 291Exercises 5.4 2935.5 Nonconstant Mass Systems 299Examples 303Exercises 5.5 3055.6 Just the Facts 310System Analysis 313Chapter 6Kinematics of Rigid Bodies Undergoing Planar Motion 3146.1 Relative Velocities on a Rigid Body 315Examples 320Exercises 6.1 3256.2 Instantaneous Center of Rotation (icr) 333Examples 335Exercises 6.2 3416.3 Rotating Reference Frames and Rigid-Body Accelerations 346Examples 350Exercises 6.3 3566.4 Relative Motion on a Rigid Body 361Examples 365Exercises 6.4 3716.5 Just the Facts 378System Analysis 380Chapter 7Kinetics of Rigid Bodies Undergoing Two-dimensional Motion 3827.1 Curvilinear Translation 384Examples 385Exercises 7.1 3927.2 Rotation about a Fixed Point 396Examples 401Exercises 7.2 4117.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 457Examples 460Exercises 7.4 4627.5 Work/Energy of Two-Dimensional Rigid Bodies 468Examples 471Exercises 7.5 4757.6 Just the Facts 482System Analysis 484Chapter 8Kinematics and Kinetics of Rigid Bodies in Three-dimensional Motion 4878.1 Spherical Coordinates 4888.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 489Examples 4938.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 495Examples 4968.4 General Motion of and on Three-Dimensional Bodies 497Examples 498Exercises 8.4 5028.5 Moments and Products of Inertia for a Three-Dimensional Body 5068.6 Parallel Axis Expressions for Inertias 508Examples 510Exercises 8.6 5118.7 Angular Momentum 513Examples 517Exercises 8.7 5208.8 Equations of Motion for a Three-Dimensional Body 521Examples 524Exercises 8.8 5268.9 Energy of Three-Dimensional Bodies 532Examples 534Exercises 8.9 5368.10 Just the Facts 537System Analysis 5417.3 General Motion 422Examples 425Exercises 7.3 444Chapter 9Vibratory Motions 5429.1 Undamped, Free Response for Single-Degree-of-Freedom Systems 543Examples 546Exercises 9.1 5499.2 Undamped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 555Examples 558Exercises 9.2 5609.3 Damped, Free Response for Single-Degree-of-Freedom Systems 563Examples 567Exercises 9.3 5689.4 Damped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 569Examples 572Exercises 9.4 5759.5 Just the Facts 576System Analysis 579Appendix ANumerical Integration Light 580Appendix BProperties of Plane and Solid Bodies 588Appendix CSome Useful Mathematical Facts 592Appendix DMaterial Densities 595Bibliography 597Index 598

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Benson H. Tongue, Ph.D., is a Professor of Mechanical Engineering at University of California-Berkeley. He received his Ph.D. from Princeton University in 1988, and currently teaches graduate and undergraduate courses in dynamics, vibrations, and control theory.Dr. Tongue has served as Associate Technical Editor of the ASME Journal of Vibration and Acoustics as a member of the ASME Committee on Dynamics of Structures and Systems. He is the recipient of the NSF Presidential Young Investigator Award, the Sigma Xi Junior Faculty award, and the Pi Tau Sigma Excellence in Teaching award. He serves as a reviewer for numerous journals and funding agencies and is the author of more than eighty publications.Sheri D. Sheppard Ph.D., is the Carnegie Foundation for the Advancement of Teaching Senior Scholar principally responsible for the Preparations for the Professions Program (PPP) engineering study. She is an Associate Professor of Mechanical Engineering at Stanford University. She received her Ph.D. from the University of Michigan in 1985.Dr. Sheppard was recently named co-principal investigator on a NSF grant to form the Deter for the Advancement of Engineering Education (CAEE). In 1999, she was named a fellow of the American Society of Mechanical Engineering (ASME) and the American Association for the Advancement of Science (AAAS). In 2004 Dr. Shepard was awarded the ASEE Chester F. Carlson Award in recognition of distinguished accomplishments in engineering education.

• Chapter 1Background and Roadmap 11.1 Newton’s Laws 21.2 How You’ll Be Approaching Dynamics 21.3 Units and Symbols 61.4 Gravitation 101.5 The Pieces of the Puzzle 11Chapter 2Motion of Translating Bodies 162.1 Straight-Line Motion 17Examples 23Exercises 2.1 282.2 Cartesian Coordinates 33Examples 38Exercises 2.2 432.3 Polar and Cylindrical Coordinates 47Examples 54Exercises 2.3 582.4 Path Coordinates 64Examples 67Exercises 2.4 712.5 Relative Motion and Constraints 76Examples 82Exercises 2.5 872.6 Just the Facts 93System Analysis 97Chapter 3Inertial Response of Translating Bodies 993.1 Cartesian Coordinates 100Examples 102Exercises 3.1 1083.2 Polar Coordinates 119Examples 120Exercises 3.2 1273.3 Path Coordinates 133Examples 134Exercises 3.3 1393.4 Linear Momentum and Linear Impulse 143Examples 145Exercises 3.4 1473.5 Angular Momentum and Angular Impulse 155Examples 158Exercises 3.5 1613.6 Orbital Mechanics 163Examples 176Exercises 3.6 1783.7 Impact 183Examples 189Exercises 3.7 1913.8 Oblique Impact 193Examples 196Exercises 3.8 2003.9 Just the Facts 203System Analysis 206Chapter 4Energetics of Translating Bodies 2094.1 Kinetic Energy 210Examples 212Exercises 4.1 2154.2 Potential Energies and Conservative Forces 220Examples 225Exercises 4.2 2314.3 Power and Efficiency 243Examples 247Exercises 4.3 2504.4 Just the Facts 255System Analysis 257Chapter 5Multibody Systems 2585.1 Force Balance and Linear Momentum 259Examples 263Exercises 5.1 2685.2 Angular Momentum 273Examples 277Exercises 5.2 2795.3 Work and Energy 282Examples 284Exercises 5.3 2875.4 Stationary Enclosures with Mass Inflow and Outflow 288Examples 291Exercises 5.4 2935.5 Nonconstant Mass Systems 299Examples 303Exercises 5.5 3055.6 Just the Facts 310System Analysis 313Chapter 6Kinematics of Rigid Bodies Undergoing Planar Motion 3146.1 Relative Velocities on a Rigid Body 315Examples 320Exercises 6.1 3256.2 Instantaneous Center of Rotation (icr) 333Examples 335Exercises 6.2 3416.3 Rotating Reference Frames and Rigid-Body Accelerations 346Examples 350Exercises 6.3 3566.4 Relative Motion on a Rigid Body 361Examples 365Exercises 6.4 3716.5 Just the Facts 378System Analysis 380Chapter 7Kinetics of Rigid Bodies Undergoing Two-dimensional Motion 3827.1 Curvilinear Translation 384Examples 385Exercises 7.1 3927.2 Rotation about a Fixed Point 396Examples 401Exercises 7.2 4117.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 457Examples 460Exercises 7.4 4627.5 Work/Energy of Two-Dimensional Rigid Bodies 468Examples 471Exercises 7.5 4757.6 Just the Facts 482System Analysis 484Chapter 8Kinematics and Kinetics of Rigid Bodies in Three-dimensional Motion 4878.1 Spherical Coordinates 4888.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 489Examples 4938.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 495Examples 4968.4 General Motion of and on Three-Dimensional Bodies 497Examples 498Exercises 8.4 5028.5 Moments and Products of Inertia for a Three-Dimensional Body 5068.6 Parallel Axis Expressions for Inertias 508Examples 510Exercises 8.6 5118.7 Angular Momentum 513Examples 517Exercises 8.7 5208.8 Equations of Motion for a Three-Dimensional Body 521Examples 524Exercises 8.8 5268.9 Energy of Three-Dimensional Bodies 532Examples 534Exercises 8.9 5368.10 Just the Facts 537System Analysis 5417.3 General Motion 422Examples 425Exercises 7.3 444Chapter 9Vibratory Motions 5429.1 Undamped, Free Response for Single-Degree-of-Freedom Systems 543Examples 546Exercises 9.1 5499.2 Undamped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 555Examples 558Exercises 9.2 5609.3 Damped, Free Response for Single-Degree-of-Freedom Systems 563Examples 567Exercises 9.3 5689.4 Damped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 569Examples 572Exercises 9.4 5759.5 Just the Facts 576System Analysis 579Appendix ANumerical Integration Light 580Appendix BProperties of Plane and Solid Bodies 588Appendix CSome Useful Mathematical Facts 592Appendix DMaterial Densities 595Bibliography 597Index 598

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