Page 15 - Dynamics of Mechanical Systems

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10.4 Power .................................................................................................................................327
10.5 Kinetic Energy ..................................................................................................................327
10.6 Work–Energy Principles..................................................................................................329
10.7 Elementary Example: A Falling Object.........................................................................332
10.8 Elementary Example: The Simple Pendulum .............................................................333
10.9 Elementary Example — A Mass–Spring System ........................................................336
10.10 Skidding Vehicle Speeds: Accident Reconstruction Analysis...................................338
10.11 A Wheel Rolling Over a Step.........................................................................................341
10.12 The Spinning Diagonally Supported Square Plate.....................................................342
10.13 Closure ...............................................................................................................................344
References (Accident Reconstruction)......................................................................................344
Problems .......................................................................................................................................344
Chapter 11 Generalized Dynamics: Kinematics and Kinetics..........................................353
11.1 Introduction.......................................................................................................................353
11.2 Coordinates, Constraints, and Degrees of Freedom ..................................................353
11.3 Holonomic and Nonholonomic Constraints ...............................................................357
11.4 Vector Functions, Partial Velocity, and Partial Angular Velocity.............................359
11.5 Generalized Forces: Applied (Active) Forces ..............................................................363
11.6 Generalized Forces: Gravity and Spring Forces .........................................................367
11.7 Example: Spring-Supported Particles in a Rotating Tube.........................................369
11.8 Forces That Do Not Contribute to the Generalized Forces ......................................375
11.9 Generalized Forces: Inertia (Passive) Forces ...............................................................377
11.10 Examples............................................................................................................................379
11.11 Potential Energy ...............................................................................................................389
11.12 Use of Kinetic Energy to Obtain Generalized Inertia Forces ...................................394
11.13 Closure ...............................................................................................................................401
References.....................................................................................................................................401
Problems .......................................................................................................................................402

Chapter 12 Generalized Dynamics: Kane’s Equations
and Lagrange’s Equations .................................................................................415
12.1 Introduction.......................................................................................................................415
12.2 Kane’s Equations..............................................................................................................415
12.3 Lagrange’s Equations ......................................................................................................423
12.4 The Triple-Rod Pendulum ..............................................................................................429
12.5 The N-Rod Pendulum .....................................................................................................433
12.6 Closure ...............................................................................................................................435
References.....................................................................................................................................436
Problems .......................................................................................................................................436
Chapter 13 Introduction to Vibrations .................................................................................439
13.1 Introduction.......................................................................................................................439
13.2 Solutions of Second-Order Differential Equations .....................................................439
13.3 The Undamped Linear Oscillator..................................................................................444
13.4 Forced Vibration of an Undamped Oscillator.............................................................446
13.5 Damped Linear Oscillator ..............................................................................................447
13.6 Forced Vibration of a Damped Linear Oscillator .......................................................449
13.7 Systems with Several Degrees of Freedom..................................................................450
13.8 Analysis and Discussion of Three-Particle Movement:
Modes of Vibration ..........................................................................................................455