Fundamentals of Dynamics and Analysis of Motion

Fundamentals of Dynamics and Analysis of Motion

by Marcelo R. M. Crespo da Silva

Paperback(First Edition, First)

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Designed for a first-year graduate-level or senior course in dynamics for students in engineering and physics, this text will also be useful for self-study and as a reference book for students working in this area. Prerequisites include previous courses in statics, calculus, and basic ordinary differential equations. The treatment stresses the fundamentals of setting up and solving dynamics problems rather than the indiscriminate use of elaborate formulas.
Topics include essential material for dynamics, kinematics and dynamics of point masses, kinematic analysis of planar mechanisms, special dynamical properties of a system of point masses, dynamics of rigid bodies in "simpler" planar motion, dynamics of rigid bodies in general motion, analytical dynamics, and vibrations and oscillations of dynamical systems. Four of the seven appendixes include tutorials on relevant software, a listing of several simulation and animation programs written by the author, as well as answers to selected problems and references for advanced study. Includes a software package available as a free download from Dover's website.

Product Details

ISBN-13: 9780486797373
Publisher: Dover Publications
Publication date: 04/21/2016
Series: Dover Books on Engineering Series
Edition description: First Edition, First
Pages: 720
Sales rank: 1,229,361
Product dimensions: 6.10(w) x 9.20(h) x 1.60(d)

About the Author

Marcelo R. M. Crespo da Silva taught at the University of Cincinnati from 1971 to 1986, after which he joined the faculty at Rensselaer Polytechnic Institute, where he is now Professor Emeritus in the Department of Mechanical, Aerospace, and Nuclear Engineering.

Table of Contents

Preface vii

Chapter 1 Essential Material Tor Dynamics 1

1.1 Vector and Scalar Quantities: A Brief Review 1

1.2 Transformation of Triads 5

1.3 Basic Operations with Vectors 8

1.4 Moment of a Vector about a Point 13

1.5 Newton's Laws of Motion 15

1.6 Kepler's Laws and Newton's Law of Universal Gravitation 17

1.7 Force of Attraction due to a Spherical Body 19

1.8 Gravitational Force, Weight, and the Meaning of Weightlessness 22

1.9 Equivalent Force Systems 23

1.10 Center of Gravity and Center of Mass 24

1.11 Free-Body Diagrams and Forces 31

1.12 Chain Ride of Differentiation and Exact Differentials 38

1.13 Some Basics on Differential Equations 41

1.14 Taylor Series Expansion and Linearization 59

1.15 Stability Analysis and Linearization 64

1.16 Multiple Degree-of-Freedom Linear Systems 66

1.17 The Routh-Hurwitz Stability Criterion 68

1.18 Introduction to the Lyapinov Stability Method 74

1.19 An Interesting Experiment 85

1.20 Problems 86

Chapter 2 Kinematics and Dynamics of Point Masses 93

2.1 How to Formulate a Dynamics Problem 93

2.2 A Note on the Reaction Force due to Springs 97

2.3 A Moment Equation Obtained from Newton's Second Law 99

2.4 Absolute Position, Velocity, and Acceleration of a Point 100

2.5 Solved Example Problems 103

2.6 Velocity and Acceleration Again and Angular Velocity 138

2.7 More Solved Example Problems 142

2.8 A Work-Energy Approach Obtained from Newton's Second Law 187

2.9 Problems 208

Chapter 3 Kinematic Analysis of Planar Mechanisms 221

3.1 Instantaneous Center of Rotation 221

3.2 The Four-Bar Mechanism 224

3.2.1 General Analysis of the Four-Bar Mechanism 225

3.2.2 Solution of Eqs. (3.2.1) and (3.2.2) 229

3.2.3 Automated Solution for the Four-Bar Mechanism 237

3.3 The Geneva Wheel Mechanism 240

3.3.1 Automated Solution for the Geneva Wheel Mechanism 248

3.4 The Slider Crank Mechanism 250

3.4.1 Automated Solution for the Slider Crank Mechanism 256

3.5 The Scotch Yoke Mechanism 258

3.6 Problems 261

Chapter 4 System of Point Masses: Special Dynamical Properties 268

4.1 Motion of the Center of Mass of a System of Point Masses 269

4.2 Time Rate of Change of Angular Momentum, and Moment 271

4.3 An Integrated Form of Newton's Second Law and of the Moment Equation 273

4.4 Detailed Analysis of the Two-Body Problem 280

4.4.1 The Meaning of the Quantity E: Kinetic and Potential Energies of the Motion 281

4.4.2 Determination of the Maximum and Minimum Values of r(t) 282

4.4.3 Solution of the Orbital Differential Equation of Motion for r in Terms of θ 285

4.4.4 Solved Example Problems 289

4.5 Automated Solution for the Two-Body Problem 293

4.6 The Restricted Three-Body Problem 295

4.6.1 Differential Equations of Motion 296

4.6.2 Equilibrium Solutions 300

4.6.3 Stability of the Equilibrium Solutions 302

4.7 Problems 307

Chapter 5 Dynamics of Rigid Bodies in "Simpler" Planar Motion 313

5.1 Degrees of Freedom of a Rigid Body 314

5.2 Types of Rigid Body Displacements 315

5.3 Dynamics of Simpler Planar Motion of a Rigid Body 317

5.4 Rolling of a Rigid Body 354

5.5 A Work-Energy Approach for Rigid Body Dynamics 369

5.6 Forces on Mechanisms 371

5.7 Problems 378

Chapter 6 Dynamics of Rigid Bodies in General Motion 396

6.1 Juxtaposition of Two Vectors: Dyadies 397

6.2 The Two Basic Vector Equations of Rigid Body Dynamics 399

6.3 Rotational Kinematics of Rigid Bodies in General Motion 400

6.3.1 Absolute Angular Momentum 401

6.3.2 The Parallel Axis Theorem 406

6.3.3 Examples Involving Moments and Products of Inertia 408

6.3.4 Principal Axes and Principal Moments of Inertia 417

6.3.5 Examples of Determination of Principal Axes and Principal Inertias 420

6.4 Euler's Differential Equations of Rotational Motion 425

6.5 Kinetic Energy and the Work-Energy Approach 427

6.6 Classical Problems 430

6.6.1 Stability of a Body Spun about One of its Principal Axes 430

6.6.2 Dynamic Balancing of a Rotating Part of a Machine 435

6.6.3 Motion of a Symmetric Top (or of a Gyroscope) 441

6.6.4 On the Nutational Motion of a Symmetric Top 453

6.7 Solved Example Problems 455

6.8 Angular Orientation of a Rigid Body: Orientation Angles 468

6.9 Angular Velocity and the Orientation Angles: Notes 485

6.10 Problems 486

Chapter 7 Analytical Dynamics 499

7.1 Virtual Variations and Virtual Displacements 500

7.2 Virtual Work and Generalized Forces, and Constraint Forces 504

7.3 The Principles of d'Alembert and of Virtual Work 516

7.4 Hamilton's Principle and Lagrange's Equation 517

7.4.1 Hamilton's Principle 518

7.4.2 Lagrange's Equation (Discrete Systems) Obtained from Hamilton's Principle 522

7.4.3 General Form of the Kinetic Energy T 525

7.5 Conservation Principles: Classical Integrals of Motion 526

7.5.1 What is an Integral of the Motion? 526

7.5.2 Integrals of Motion Obtained from Lagrange's Equation 527

7.5.3 General Form of the Hamiltoman for Any Problem 530

7.6 A Brief Summary 531

7.7 Solved Example Problems 532

7.8 Constraints, and Lagrange's Equation with Constraints 553

7.8.1 Constraints 554

7.8.2 Lagiauge's Equation in the Presence of Constraints 559

7.9 Solved Example Problems with Constraints 561

7.10 Problems 572

Chapter 8 Vibrations/Oscillations of Dynamical Systems 579

8.1 What Was Already Presented on Vibrations/Oscillations in Previous Chapters 579

8.2 Response of a Linear System to Sinusoidal Forcing Functions 580

8.3 Analysis of a Vibration Absorber Device 584

8.3.1 Homogeneous Solution and Stability of the Equilibrium 586

8.3.2 Particular Solution: Response to a Sinusoidal Force 586

8.4 Analysis of the Foucault Pendulun 588

8.4.1 Problem Description 588

8.4.2 Formulation Using Rectangular Coordinates 588

Appendix A Scilab, Matlab, and Simulink Tutorials 596

A.1 Introduction to Scilab and Matlab 596

A.1.1 Plotting 605

A.1.2 Numerical Solution of Ordinary Differential Equations 609

A.1.3 Animation 612

A.2 Introduction to Simulink 613

Appendix B Sequential Rotations, Angular Velocity, and Acceleration 624

B.1 Sequential Rotations and Angular Velocity 624

B.2 A Note on the General Form of Acceleration Expressions 627

Appendix C Properties of the Inertia Matrix of a Body 630

Appendix D Suggested Computer Lab Assignments 635

Appendix E Scilab and Matlab Programs 645

E.1 Scilab Programs 647

E.2 Matlab Programs 671

Appendix F Answer to Selected Problems 695

Appendix G Some References for Advanced Studies 699

Index 701

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