Fundamentals of Applied Dynamics
by Williams Jr.
ISBN: 9780262039710 | Copyright 2019
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An introductory engineering textbook by an award-winning MIT professor that covers the history of dynamics and the dynamical analyses of mechanical, electrical, and electromechanical systems.
This introductory textbook offers a distinctive blend of the modern and the historical, seeking to encourage an appreciation for the history of dynamics while also presenting a framework for future learning. The text presents engineering mechanics as a unified field, emphasizing dynamics but integrating topics from other disciplines, including design and the humanities.
The book begins with a history of mechanics suitable for an undergraduate overview. Subsequent chapters cover such topics as three-dimensional kinematics; the direct approach, also known as vectorial mechanics or the momentum approach; the indirect approach, also called Lagrangian dynamics or variational dynamics; an expansion of the momentum and Lagrangian formulations to extended bodies; lumped-parameter electrical and electromagnetic devices; and equations of motion for one-dimensional continuum models. The book is unique in covering both Lagrangian dynamics and vibration analysis. The principles covered are relatively few and easy to articulate; the examples are rich and broad. Summary tables, often in the form of flowcharts, appear throughout. End-of-chapter problems begin at the elementary level and become increasingly difficult. Appendixes provide theoretical and mathematical support for the main text.
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DEDICATION (pg. iii) | |
BESTOWAL (pg. v) | |
ABOUT THE AUTHOR (pg. vii) | |
ACKNOWLEDGMENTS (pg. ix) | |
PREFACE (pg. xi) | |
CONTENTS (pg. xix) | |
1 OUR NICHE IN THE COSMOS (pg. 1) | |
1-1 INTRODUCTION (pg. 1) | |
1-2 WHY HISTORY? (pg. 3) | |
1-3 IMPORTANCE OF MATHEMATICS IN THE DEVELOPMENT OF MECHANICS (pg. 3) | |
1-4 OUR SOURCES FROM ANTIQUITY: GETTING THE MESSAGE FROM THERE TO HERE (pg. 4) | |
1-4.1 Invention of Writing (pg. 5) | |
1-4.2 Hieroglyphics (pg. 6) | |
1-4.3 Cuneiform (pg. 7) | |
1-4.4 Ancient Egyptian Papyri (pg. 7) | |
1-4.5 Mesopotamian Clay Tablets (pg. 9) | |
1-5 ANCIENT EGYPTIAN ASTRONOMY AND MATHEMATICS (pg. 9) | |
1-5.1 Ancient Egyptian Astronomy (pg. 10) | |
1-5.2 Ancient Egyptian Mathematics (pg. 11) | |
1-6 MESOPOTAMIAN ASTRONOMY AND MATHEMATICS (pg. 14) | |
1-6.1 Mesopotamian Astronomy (pg. 15) | |
1-6.2 Mesopotamian Mathematics (pg. 15) | |
1-7 MATHEMATICS OF THE MAYANS, INDIANS, ARABS, AND CHINESE (pg. 16) | |
1-8 THE FIRST GREAT ENGINEERING SOCIETY (pg. 19) | |
1-9 ADVERSE CRITICISM OF ANCIENT EGYPTIAN AND MESOPOTAMIAN MATHEMATICS (pg. 24) | |
1-10 EVOLUTION THROUGH THE HELLENIC ERA (pg. 29) | |
1-11 THE UNIFICATION OF CELESTIAL AND TERRESTRIAL MOTION (pg. 31) | |
1-11.1 Celestial Motion (pg. 31) | |
1-11.2 Terrestrial Motion (pg. 44) | |
1-11.3 Unification (pg. 45) | |
1-12 VARIATIONAL PRICIPLES IN DYNAMICS (pg. 47) | |
1-13 THE INTERNATIONALISM OF DYNAMICS (pg. 52) | |
1-14 OUR NICHE IN THE COSMOS (pg. 53) | |
2 DESIGN, MODELING, AND FORMULATION OF EQUATIONS OF MOTION (pg. 55) | |
2-1 INTRODUCTION (pg. 55) | |
2-2 DESIGN AND MODELING (pg. 56) | |
2-2.1 The Design Process (pg. 56) | |
2-2.2 The Modeling Process (pg. 57) | |
2-2.3 Our More Modest Goals (pg. 58) | |
2-3 DIRECT AND INDIRECT APPROACHES FOR FORMULATION OF EQUATIONS OF MOTION (pg. 59) | |
3 KINEMATICS (pg. 68) | |
3-1 INTRODUCTION (pg. 68) | |
3-2 POSITION, VELOCITY, AND ACCELERATION (pg. 69) | |
3-3 PLANE KINEMATICS OF RIGID BONES (pg. 75) | |
3-3.1 The General Motion of a Rigid Body (pg. 75) | |
3-3.2 Types of Plane Motion of a Rigid Body (pg. 76) | |
3-3.3 Angular Displacement, Angular Velocity, and Angular Acceleration (pg. 77) | |
3-3.4 A Cautionary Note about Finite Rotations (pg. 83) | |
3-4 TIME RATE OF CHANGE OF VECTOR IN ROTATING FRAME (pg. 85) | |
3-5 KINEMATIC ANALYSIS UTILIZING INTERMEDIATE FRAMES (pg. 90) | |
3-6 GENERALIZATIONS OF KINEMATIC EXPRESSIONS (pg. 108) | |
4 MOMENTUM FORMULATION FOR SYSTEMS OF PARTICLES (pg. 135) | |
4-1 INTRODUCTION (pg. 135) | |
4-2 THE FUNDAMENTAL PHYSICS (pg. 136) | |
4-2.1 Newton’s Laws of Motion (pg. 136) | |
4-2.2 A Particle (pg. 137) | |
4-2.3 Linear Momentum and Force (pg. 138) | |
4-2.4 Inertial Reference Frames (pg. 139) | |
4-2.5 The Universal Law of Gravitation (pg. 140) | |
4-3 TORQUE AND ANGULAR MOMENTUM FOR A PARTICLE (pg. 141) | |
4-4 FORMULATION OF EQUATIONS OF MOTION: EXAMPLES (pg. 144) | |
4-4.1 Problems of Particle Dynamics of the First Kind (pg. 145) | |
4-4.2 Problems of Particle Dynamics of the Second Kind (pg. 151) | |
5 VARIATIONAL FORMULATION FOR SYSTEMS OF PARTICLES (pg. 179) | |
5-1 INTRODUCTION (pg. 179) | |
5-2 FORMULATION OF EQUATIONS OF MOTION (pg. 180) | |
5-3 WORK AND STATE FUNCTIONS (pg. 181) | |
5-3.1 Work (pg. 182) | |
5-3.2 Kinetic State Functions (pg. 183) | |
5-3.3 Potential State Functions (pg. 185) | |
5-3.4 Energy and Coenergy (pg. 189) | |
5-4 GENERALIZED VARIABLES AND VARIATIONAL CONCEPTS (pg. 190) | |
5-4.1 Generalized Coordinates (pg. 190) | |
5-4.2 Admissible Variations, Degrees of Freedom, Geometric Contraints, and Holonomicity (pg. 195) | |
5-4.3 Variational Principles in Mechanics (pg. 201) | |
5-4.4 Generalized Velocities and Generalized Forces for Holonomic Systems (pg. 205) | |
5-5 EQUATIONS OF MOTION FOR HOLONOMIC MECHANICAL SYSTEMS VIA VARIATIONAL PRINCIPLES (pg. 213) | |
5-6 WORK-ENERGY RELATION (pg. 238) | |
5-7 NATURE OF LAGRANGIAN DYNAMICS (pg. 241) | |
Problems for Chapter 5 (pg. 243) | |
6 DYNAMICS OF SYSTEMS CONTAINING RIGID BODIES (pg. 268) | |
6-1 INTRODUCTION (pg. 268) | |
6-2 MOMENTUM PRINCIPLES FOR RIGID BODIES (pg. 269) | |
6-2.1 Review of Solids in Equilibrium and Particle Dynamics (pg. 270) | |
6-2.2 Models of Rigid Bodies (pg. 271) | |
6-2.3 Momentum Principles for Extended Bodies: The Newton-Euler Equations (pg. 272) | |
6-2.4 Momentum Principles for Rigid Bodies Modeled as Systems of Particles (pg. 273) | |
6-2.5 Momentum Principles for Rigid Bodies Modeled as Continua (pg. 275) | |
6-3 DYNAMIC PROPERTIES OF RIGID BODIES (pg. 279) | |
6-3.1 The Inertia Factor (pg. 279) | |
6-3.2 Parallel-Axes Theorem (pg. 290) | |
6-3.3 Principal Directions and Principal Moments of Inertia (pg. 296) | |
6-3.4 Uses of Mass Symmetry (pg. 298) | |
6-4 DYNAMICS OF RIGID BODIES VIA DIRECT APPROACH (pg. 303) | |
6-5 LAGRANGIAN FOR RIGID BODIES (pg. 308) | |
6-5.1 Kinetic Coenergy Function for Rigid Body (pg. 308) | |
6-5.2 Potential Energy Function for Rigid Body (pg. 310) | |
6-6 EQUATIONS OF MOTION FOR SYSTEMS CONTAINING RIGID BODIES IN PLANE MOTION (pg. 311) | |
Problems for Chapter 6 (pg. 334) | |
7 DYNAMICS OF ELECTRICAL AND ELECTROMECHANICAL SYSTEMS (pg. 366) | |
7-1 INTRODUCTION (pg. 366) | |
7-2 FORMULATION OF EQUATIONS OF MOTION FOR ELECTRICAL NETWORKS (pg. 369) | |
7-3 CONSTITUTIVE RELATIONS FOR CIRCUIT ELEMENTS (pg. 371) | |
7-3.1 Passive Elements (pg. 371) | |
7-3.2 Active Electrical Elements (pg. 376) | |
7-4 HAMILTON’S PRINCIPLE AND LAGRANGE’S EQUATIONS FOR ELECTRICAL NETWORKS (pg. 380) | |
7-4.1 Generalized Charge Variables (pg. 380) | |
7-4.2 Generalized Flux Linkage Variables (pg. 382) | |
7-4.3 Work Expressions (pg. 383) | |
7-4.4 Summary of Lumped-Parameter Offering of Variational Electricity (pg. 386) | |
7-4.5 Examples (pg. 386) | |
7-5 CONSTITUTIVE RELATIONS FOR TRANSDUCERS (pg. 407) | |
7-5.1 Ideal Movable-Plate Capacitor (pg. 408) | |
7-5.2 Electrically Linear Moveable-Plate Capacitor (pg. 410) | |
7-5.3 Ideal Movable-Core Inductor (pg. 412) | |
7-5.4 Magnetically Linear Movable-Core Inductor (pg. 413) | |
7-6 HAMILTON’S PRINCIPLE AND LAGRANGE’S EQUATIONS FOR ELECTROMECHANICAL SYSTEMS (pg. 415) | |
7-6.1 Displacement-Charge Variables Formulation (pg. 416) | |
7-6.2 Displacement-Flux Linkage Variables Formulation (pg. 417) | |
7-6.3 Examples (pg. 419) | |
7-7 ANOTHER LOOK AT LAGRANGIAN DYNAMICS (pg. 428) | |
Problems for Chapter 7 (pg. 429) | |
8 VIBRATION OF LINEAR LUMPED-PARAMETER SYSTEMS (pg. 439) | |
8-1 INTRODUCTION (pg. 439) | |
8-2 SINGLE-DEGREE-OF-FREEDOM FIRST-ORDER SYSTEMS (pg. 440) | |
8-2.1 Free Response (pg. 441) | |
8-2.2 Step Response (pg. 444) | |
8-2.3 Ramp Response (pg. 446) | |
8-2.4 Harmonic Response (pg. 449) | |
8-2.5 Summary of Responses for Single-Degree-of-Freedom First-Order Systems (pg. 459) | |
8-3 SINGLE-DEGREE-OF-FREEDOM SECOND-ORDER SYSTEMS (pg. 460) | |
8-3.1 Free Response (pg. 461) | |
8-3.2 Natural Frequency via Static Deflection (pg. 467) | |
8-3.3 Logarithmic Decrement (pg. 468) | |
8-3.4 Energy Loss of Free Vibration (pg. 471) | |
8-3.5 Harmonic Response (pg. 472) | |
8-3.6 Summary of Responses for Single-Degree-of-Freedom Second-Order Systems (pg. 498) | |
8-4 TWO-DEGREE-OF-FREEDOM SECOND-ORDER SYSTEMS (pg. 500) | |
8-4.1 Natural Modes of Vibration (pg. 501) | |
8-4.2 Response to Initial Conditions (pg. 514) | |
8-4.3 Harmonic Response (pg. 527) | |
8-5 STABILITY OF NONLINEAR SYSTEMS (pg. 541) | |
Problems for Chapter 8 (pg. 557) | |
9 DYNAMICS OF CONTINUOUS SYSTEMS (pg. 576) | |
9-1 INTRODUCTION (pg. 576) | |
9-2 EQUATIONS OF MOTION (pg. 578) | |
9-2.1 Longitudinal Motion of System Containing Rod (pg. 579) | |
9-2.2 Twisting Motion of System Containing Shaft (pg. 586) | |
9-2.3 Electric Transmission Line (pg. 589) | |
9-2.4 Flexural Motion of System Containing Beam (pg. 594) | |
9-2.5 Summaries (pg. 602) | |
9-3 NATURAL MODES OF VIBRATION (pg. 607) | |
9-3.1 Method of Separation Variables (pg. 608) | |
9-3.2 Time Response (pg. 610) | |
9-3.3 Eigenfunctions for Second-Order Systems (pg. 612) | |
9-3.4 Eigenfunctions for Fourth-Order Systems (pg. 620) | |
9-3.5 General Solutions for Free Undamped Vibration (pg. 633) | |
9-4 RESPONSE TO INITIAL CONDITIONS (pg. 636) | |
9-4.1 An Example: Release of Compressed Rod (pg. 636) | |
9-4.2 An Example: Shaft Stopped after Rotation (pg. 647) | |
9-4.3 An Example: Sliding-Free Beam Initially Bent (pg. 650) | |
9-5 RESPONSE TO HARMONIC EXCITATIONS (pg. 660) | |
9-5.1 An Example: Specified Harmonic Motion of Boundary (pg. 660) | |
9-5.2 An Example: Distributed Harmonic Force (pg. 662) | |
9-5.3 An Example: Harmonic Force on Boundary (pg. 665) | |
9-6 SUMMARIES (pg. 672) | |
Problems for Chapter 9 (pg. 673) | |
BIBLIOGRAPHY (pg. 684) | |
1 Historical (pg. 684) | |
2 Astronomy (pg. 686) | |
3 Design, Systems, and Modeling (pg. 686) | |
4 Elementary Dynamics (pg. 686) | |
5 Intermediate/Advanced Dynamics (pg. 686) | |
6 Hamilton’s Law of Varying Action and Hamilton’s Principle (pg. 687) | |
7 Electric and Electromechanical Systems (pg. 687) | |
8 Vibration (pg. 687) | |
APPENDIX A: FINITE ROTATION (pg. 688) | |
A-1 CHANGE IN POSITION VECTOR DUE TO FINITE ROTATION (pg. 688) | |
A-2 FINITE ROTATIONS ARE NOT VECTORS (pg. 690) | |
A-3 DO ROTATIONS EVER BEHAVE AS VECTORS? (pg. 692) | |
A-3.1 Infinitesimal Rotations Are Vectors (pg. 692) | |
A-3.2 Consecutive Finite Rotations about a Common Axis Are Vectors (pg. 692) | |
APPENDIX B: GENERAL KINEMATIC ANALYSIS (pg. 694) | |
B-1 ALL ANGULAR VELOCITIES DEFINED WITH RESPECT TO FIXED REFERENCE FRAME (CASE 1) (pg. 694) | |
B-2 EACH ANGULAR VELOCITY DEFINED WITH RESPECT TO IMMEDIATELY PRECEDING FRAME (CASE 2) (pg. 698) | |
APPENDIX C: MOMENTUM PRINCIPLES FOR SYSTEMS OF PARTICLES (pg. 705) | |
C-1 ASSERTED MOMENTUM PRINCIPLES (pg. 705) | |
C-2 PRINCIPLES FOR SINGLE PARTICLE (pg. 706) | |
C-3 PRINCIPLES FOR SYSTEM OF PARTICLES (pg. 707) | |
C-3.1 Asserted System Momentum Principles (pg. 708) | |
C-3.2 System Momentum Principles Derived from Particle Momentum Principles (pg. 709) | |
C-3.3 Conditions on Internal Forces (pg. 711) | |
C-3.4 Relationships between Momentum Principles and Conditions on Internal Forces (pg. 712) | |
C-3.5 Linear Momentum Principle in Terms of Centroidal Motion (pg. 714) | |
C-3.6 Angular Momentum Principle about Arbitrary Point (pg. 715) | |
C-3.7 System of Particle Model in Continuum Limit (pg. 717) | |
C-4 ANGULAR MOMENTUM PRINCIPLE IN NONINERTIAL INTERMEDIATE FRAME (pg. 719) | |
APPENDIX D: ELEMENTARY RESULTS OF THE CALCULUS OF VARIATIONS (pg. 728) | |
D-1 INTRODUCTION (pg. 728) | |
D-2 SUMMARY OF ELEMENTARY RESULTS (pg. 730) | |
D-3 EULER EQUATION: NECESSARY CONDITION FOR A VARIATIONAL INDICATOR TO VANISH (pg. 734) | |
APPENDIX E: SOME FORMULATIONS OF THE PRINCIPLES OF HAMILTON (pg. 737) | |
E-1 MECHANICAL FORMULATIONS (pg. 737) | |
E-1.1 Hamilton’s Law of Varying Action (pg. 740) | |
E-1.2 Hamilton’s Principle (pg. 741) | |
E-1.3 Lagrange’s Equations (pg. 742) | |
E-1.4 Discussion (pg. 743) | |
E-2 HAMILTON’S PRINCIPLE FOR ELECTROMECHANICAL SYSTEMS USING A DISPLACEMENT-CHARGE FORMULATION (pg. 744) | |
E-3 HAMILTON’S PRINCIPLE FOR ELECTROMECHANICAL SYSTEMS USING A DISPLACEMENT-FLUX LINKAGE FORMULATION (pg. 747) | |
E-4 WORK-ENERGY RELATION DERIVED FROM LAGRANGE’S EQUATIONS (pg. 749) | |
APPENDIX F: LAGRANGE’S FORM OF D’ALEMBERT’S PRINCIPLE (pg. 754) | |
F-1 FUNDAMENTAL CONCEPTS AND DERIVATIONS (pg. 754) | |
F-2 EXAMPLES (pg. 757) | |
APPENDIX G: A BRIEF REVIEW OF ELECTROMAGNETIC (EM) THEORY AND APPROXIMATIONS (pg. 763) | |
G-1 MAXWELL’S EQUATIONS: COMPLETE FORM (pg. 763) | |
G-1.1 Integral Form (pg. 763) | |
G-1.2 Differential Form (pg. 765) | |
G-2 MAXWELL’S EQUATIONS: ELECTROSTATICS AND MAGNETOSTATICS (pg. 765) | |
G-3 MAXWELL’S EQUATIONS: ELECTROQUASISTATICS AND MAGNETOQUASISTATICS (pg. 766) | |
G-3.1 Electroquasistatics (pg. 766) | |
G-3.2 Magnetoquasistatics (pg. 768) | |
G-4 ENERGY STORAGE IN ELECTROQUASISTATICS AND MAGNETOQUASISTATICS (pg. 770) | |
G-4.1 Energy Storage in Electroquasistatics (pg. 771) | |
G-4.2 Energy Storage in Magnetoquasistatics (pg. 773) | |
G-5 KIRCHHOFF’S “LAWS” (pg. 774) | |
G-5.1 Kirchhoff’s Current “Law” (pg. 774) | |
G-5.2 Kirchhoff’s Voltage “Law” (pg. 775) | |
G-5.3 Summary (pg. 776) | |
APPENDIX H: COMPLEX NUMBERS AND SOME USEFUL FORMULAS OF COMPLEX VARIABLES AND TRIGONOMETRY (pg. 777) | |
H-1 INTRODUCTION (pg. 777) | |
H-2 ELEMENTARY ALGEBRAIC OPERATIONS OF COMPLEX NUMBERS (pg. 780) | |
H-3 COMPLEX CONJUGATES (pg. 781) | |
H-4 A USEFUL FORMULA OF COMPLEX VARIABLES (pg. 782) | |
H-5 USE OF COMPLEX VARIABLES IN HARMONIC RESPONSE ANALYSES (pg. 787) | |
H-6 USEFUL FORMULAS OF TRIGONOMETRY (pg. 796) | |
APPENDIX I: TEMPORAL FUNCITON FOR SYNCHRONOUS MOTION OF TQO-DEGREE-OF-FREEDOM SYSTEMS (pg. 800) | |
I-1 FREE UNDAMPED EQUATIONS OF MOTION (pg. 800) | |
I-2 SYNHRONUS MOTION (pg. 800) | |
I-3 GENERAL TEMPORAL SOLUTION (pg. 801) | |
I-4 SPECIAL (SEMIDEFINITE) TEMPORAL SOLUTION (pg. 803) | |
I-5 GENERALIZATION TO SYSTEMS HAVING MORE DEGREES OF FREEDOM (pg. 803) | |
APPENDIX J: STABILITY ANALYSES OF NONLINEAR SYSTEMS (pg. 804) | |
J-1 STATE-SPACE STABILITY FORMULATION (pg. 804) | |
J-1.1 State-Space Representation of Equations of Motion (pg. 804) | |
J-1.2 Equilibrium States (pg. 806) | |
J-1.3 Linearization about Equilibrium States (pg. 808) | |
J-1.4 Concept and Types of Stability (pg. 809) | |
J-1.5 Stability of Linearized Systems (pg. 811) | |
J-1.6 Local Stability of Nonlinear Systems (pg. 814) | |
J-1.7 Nonllunear Stability Analyses (pg. 815) | |
J-1.8 Summary of State-Space Stability Analysis (pg. 815) | |
J-2 NONLINEAR STABILITY ANALYSIS FOR CONSERVATIVE SYSTEMS (pg. 816) | |
APPENDIX K: STRAIN ENERGY FUNCTIONS (pg. 822) | |
K-1 CONCEPT (pg. 822) | |
K-2 STRAIN ENERGY DENSITY FUNCTION (pg. 822) | |
K-3 STRAIN ENERGY FUNCTION (pg. 824) | |
K-4 EXAMPLES (pg. 825) | |
ANSWERS TO MOST OF THE ODD-NUMBERED PROBLEMS (pg. 833) | |
LIST OF TABLES (pg. 843) | |
KEY DYNAMICAL PRINCIPLES, FORMULAS, & CONVERSION FACTORS (pg. 846) | |
INDEX (pg. 851) | |
DEDICATION (pg. iii) | |
BESTOWAL (pg. v) | |
ABOUT THE AUTHOR (pg. vii) | |
ACKNOWLEDGMENTS (pg. ix) | |
PREFACE (pg. xi) | |
CONTENTS (pg. xix) | |
1 OUR NICHE IN THE COSMOS (pg. 1) | |
1-1 INTRODUCTION (pg. 1) | |
1-2 WHY HISTORY? (pg. 3) | |
1-3 IMPORTANCE OF MATHEMATICS IN THE DEVELOPMENT OF MECHANICS (pg. 3) | |
1-4 OUR SOURCES FROM ANTIQUITY: GETTING THE MESSAGE FROM THERE TO HERE (pg. 4) | |
1-4.1 Invention of Writing (pg. 5) | |
1-4.2 Hieroglyphics (pg. 6) | |
1-4.3 Cuneiform (pg. 7) | |
1-4.4 Ancient Egyptian Papyri (pg. 7) | |
1-4.5 Mesopotamian Clay Tablets (pg. 9) | |
1-5 ANCIENT EGYPTIAN ASTRONOMY AND MATHEMATICS (pg. 9) | |
1-5.1 Ancient Egyptian Astronomy (pg. 10) | |
1-5.2 Ancient Egyptian Mathematics (pg. 11) | |
1-6 MESOPOTAMIAN ASTRONOMY AND MATHEMATICS (pg. 14) | |
1-6.1 Mesopotamian Astronomy (pg. 15) | |
1-6.2 Mesopotamian Mathematics (pg. 15) | |
1-7 MATHEMATICS OF THE MAYANS, INDIANS, ARABS, AND CHINESE (pg. 16) | |
1-8 THE FIRST GREAT ENGINEERING SOCIETY (pg. 19) | |
1-9 ADVERSE CRITICISM OF ANCIENT EGYPTIAN AND MESOPOTAMIAN MATHEMATICS (pg. 24) | |
1-10 EVOLUTION THROUGH THE HELLENIC ERA (pg. 29) | |
1-11 THE UNIFICATION OF CELESTIAL AND TERRESTRIAL MOTION (pg. 31) | |
1-11.1 Celestial Motion (pg. 31) | |
1-11.2 Terrestrial Motion (pg. 44) | |
1-11.3 Unification (pg. 45) | |
1-12 VARIATIONAL PRICIPLES IN DYNAMICS (pg. 47) | |
1-13 THE INTERNATIONALISM OF DYNAMICS (pg. 52) | |
1-14 OUR NICHE IN THE COSMOS (pg. 53) | |
2 DESIGN, MODELING, AND FORMULATION OF EQUATIONS OF MOTION (pg. 55) | |
2-1 INTRODUCTION (pg. 55) | |
2-2 DESIGN AND MODELING (pg. 56) | |
2-2.1 The Design Process (pg. 56) | |
2-2.2 The Modeling Process (pg. 57) | |
2-2.3 Our More Modest Goals (pg. 58) | |
2-3 DIRECT AND INDIRECT APPROACHES FOR FORMULATION OF EQUATIONS OF MOTION (pg. 59) | |
3 KINEMATICS (pg. 68) | |
3-1 INTRODUCTION (pg. 68) | |
3-2 POSITION, VELOCITY, AND ACCELERATION (pg. 69) | |
3-3 PLANE KINEMATICS OF RIGID BONES (pg. 75) | |
3-3.1 The General Motion of a Rigid Body (pg. 75) | |
3-3.2 Types of Plane Motion of a Rigid Body (pg. 76) | |
3-3.3 Angular Displacement, Angular Velocity, and Angular Acceleration (pg. 77) | |
3-3.4 A Cautionary Note about Finite Rotations (pg. 83) | |
3-4 TIME RATE OF CHANGE OF VECTOR IN ROTATING FRAME (pg. 85) | |
3-5 KINEMATIC ANALYSIS UTILIZING INTERMEDIATE FRAMES (pg. 90) | |
3-6 GENERALIZATIONS OF KINEMATIC EXPRESSIONS (pg. 108) | |
4 MOMENTUM FORMULATION FOR SYSTEMS OF PARTICLES (pg. 135) | |
4-1 INTRODUCTION (pg. 135) | |
4-2 THE FUNDAMENTAL PHYSICS (pg. 136) | |
4-2.1 Newton’s Laws of Motion (pg. 136) | |
4-2.2 A Particle (pg. 137) | |
4-2.3 Linear Momentum and Force (pg. 138) | |
4-2.4 Inertial Reference Frames (pg. 139) | |
4-2.5 The Universal Law of Gravitation (pg. 140) | |
4-3 TORQUE AND ANGULAR MOMENTUM FOR A PARTICLE (pg. 141) | |
4-4 FORMULATION OF EQUATIONS OF MOTION: EXAMPLES (pg. 144) | |
4-4.1 Problems of Particle Dynamics of the First Kind (pg. 145) | |
4-4.2 Problems of Particle Dynamics of the Second Kind (pg. 151) | |
5 VARIATIONAL FORMULATION FOR SYSTEMS OF PARTICLES (pg. 179) | |
5-1 INTRODUCTION (pg. 179) | |
5-2 FORMULATION OF EQUATIONS OF MOTION (pg. 180) | |
5-3 WORK AND STATE FUNCTIONS (pg. 181) | |
5-3.1 Work (pg. 182) | |
5-3.2 Kinetic State Functions (pg. 183) | |
5-3.3 Potential State Functions (pg. 185) | |
5-3.4 Energy and Coenergy (pg. 189) | |
5-4 GENERALIZED VARIABLES AND VARIATIONAL CONCEPTS (pg. 190) | |
5-4.1 Generalized Coordinates (pg. 190) | |
5-4.2 Admissible Variations, Degrees of Freedom, Geometric Contraints, and Holonomicity (pg. 195) | |
5-4.3 Variational Principles in Mechanics (pg. 201) | |
5-4.4 Generalized Velocities and Generalized Forces for Holonomic Systems (pg. 205) | |
5-5 EQUATIONS OF MOTION FOR HOLONOMIC MECHANICAL SYSTEMS VIA VARIATIONAL PRINCIPLES (pg. 213) | |
5-6 WORK-ENERGY RELATION (pg. 238) | |
5-7 NATURE OF LAGRANGIAN DYNAMICS (pg. 241) | |
Problems for Chapter 5 (pg. 243) | |
6 DYNAMICS OF SYSTEMS CONTAINING RIGID BODIES (pg. 268) | |
6-1 INTRODUCTION (pg. 268) | |
6-2 MOMENTUM PRINCIPLES FOR RIGID BODIES (pg. 269) | |
6-2.1 Review of Solids in Equilibrium and Particle Dynamics (pg. 270) | |
6-2.2 Models of Rigid Bodies (pg. 271) | |
6-2.3 Momentum Principles for Extended Bodies: The Newton-Euler Equations (pg. 272) | |
6-2.4 Momentum Principles for Rigid Bodies Modeled as Systems of Particles (pg. 273) | |
6-2.5 Momentum Principles for Rigid Bodies Modeled as Continua (pg. 275) | |
6-3 DYNAMIC PROPERTIES OF RIGID BODIES (pg. 279) | |
6-3.1 The Inertia Factor (pg. 279) | |
6-3.2 Parallel-Axes Theorem (pg. 290) | |
6-3.3 Principal Directions and Principal Moments of Inertia (pg. 296) | |
6-3.4 Uses of Mass Symmetry (pg. 298) | |
6-4 DYNAMICS OF RIGID BODIES VIA DIRECT APPROACH (pg. 303) | |
6-5 LAGRANGIAN FOR RIGID BODIES (pg. 308) | |
6-5.1 Kinetic Coenergy Function for Rigid Body (pg. 308) | |
6-5.2 Potential Energy Function for Rigid Body (pg. 310) | |
6-6 EQUATIONS OF MOTION FOR SYSTEMS CONTAINING RIGID BODIES IN PLANE MOTION (pg. 311) | |
Problems for Chapter 6 (pg. 334) | |
7 DYNAMICS OF ELECTRICAL AND ELECTROMECHANICAL SYSTEMS (pg. 366) | |
7-1 INTRODUCTION (pg. 366) | |
7-2 FORMULATION OF EQUATIONS OF MOTION FOR ELECTRICAL NETWORKS (pg. 369) | |
7-3 CONSTITUTIVE RELATIONS FOR CIRCUIT ELEMENTS (pg. 371) | |
7-3.1 Passive Elements (pg. 371) | |
7-3.2 Active Electrical Elements (pg. 376) | |
7-4 HAMILTON’S PRINCIPLE AND LAGRANGE’S EQUATIONS FOR ELECTRICAL NETWORKS (pg. 380) | |
7-4.1 Generalized Charge Variables (pg. 380) | |
7-4.2 Generalized Flux Linkage Variables (pg. 382) | |
7-4.3 Work Expressions (pg. 383) | |
7-4.4 Summary of Lumped-Parameter Offering of Variational Electricity (pg. 386) | |
7-4.5 Examples (pg. 386) | |
7-5 CONSTITUTIVE RELATIONS FOR TRANSDUCERS (pg. 407) | |
7-5.1 Ideal Movable-Plate Capacitor (pg. 408) | |
7-5.2 Electrically Linear Moveable-Plate Capacitor (pg. 410) | |
7-5.3 Ideal Movable-Core Inductor (pg. 412) | |
7-5.4 Magnetically Linear Movable-Core Inductor (pg. 413) | |
7-6 HAMILTON’S PRINCIPLE AND LAGRANGE’S EQUATIONS FOR ELECTROMECHANICAL SYSTEMS (pg. 415) | |
7-6.1 Displacement-Charge Variables Formulation (pg. 416) | |
7-6.2 Displacement-Flux Linkage Variables Formulation (pg. 417) | |
7-6.3 Examples (pg. 419) | |
7-7 ANOTHER LOOK AT LAGRANGIAN DYNAMICS (pg. 428) | |
Problems for Chapter 7 (pg. 429) | |
8 VIBRATION OF LINEAR LUMPED-PARAMETER SYSTEMS (pg. 439) | |
8-1 INTRODUCTION (pg. 439) | |
8-2 SINGLE-DEGREE-OF-FREEDOM FIRST-ORDER SYSTEMS (pg. 440) | |
8-2.1 Free Response (pg. 441) | |
8-2.2 Step Response (pg. 444) | |
8-2.3 Ramp Response (pg. 446) | |
8-2.4 Harmonic Response (pg. 449) | |
8-2.5 Summary of Responses for Single-Degree-of-Freedom First-Order Systems (pg. 459) | |
8-3 SINGLE-DEGREE-OF-FREEDOM SECOND-ORDER SYSTEMS (pg. 460) | |
8-3.1 Free Response (pg. 461) | |
8-3.2 Natural Frequency via Static Deflection (pg. 467) | |
8-3.3 Logarithmic Decrement (pg. 468) | |
8-3.4 Energy Loss of Free Vibration (pg. 471) | |
8-3.5 Harmonic Response (pg. 472) | |
8-3.6 Summary of Responses for Single-Degree-of-Freedom Second-Order Systems (pg. 498) | |
8-4 TWO-DEGREE-OF-FREEDOM SECOND-ORDER SYSTEMS (pg. 500) | |
8-4.1 Natural Modes of Vibration (pg. 501) | |
8-4.2 Response to Initial Conditions (pg. 514) | |
8-4.3 Harmonic Response (pg. 527) | |
8-5 STABILITY OF NONLINEAR SYSTEMS (pg. 541) | |
Problems for Chapter 8 (pg. 557) | |
9 DYNAMICS OF CONTINUOUS SYSTEMS (pg. 576) | |
9-1 INTRODUCTION (pg. 576) | |
9-2 EQUATIONS OF MOTION (pg. 578) | |
9-2.1 Longitudinal Motion of System Containing Rod (pg. 579) | |
9-2.2 Twisting Motion of System Containing Shaft (pg. 586) | |
9-2.3 Electric Transmission Line (pg. 589) | |
9-2.4 Flexural Motion of System Containing Beam (pg. 594) | |
9-2.5 Summaries (pg. 602) | |
9-3 NATURAL MODES OF VIBRATION (pg. 607) | |
9-3.1 Method of Separation Variables (pg. 608) | |
9-3.2 Time Response (pg. 610) | |
9-3.3 Eigenfunctions for Second-Order Systems (pg. 612) | |
9-3.4 Eigenfunctions for Fourth-Order Systems (pg. 620) | |
9-3.5 General Solutions for Free Undamped Vibration (pg. 633) | |
9-4 RESPONSE TO INITIAL CONDITIONS (pg. 636) | |
9-4.1 An Example: Release of Compressed Rod (pg. 636) | |
9-4.2 An Example: Shaft Stopped after Rotation (pg. 647) | |
9-4.3 An Example: Sliding-Free Beam Initially Bent (pg. 650) | |
9-5 RESPONSE TO HARMONIC EXCITATIONS (pg. 660) | |
9-5.1 An Example: Specified Harmonic Motion of Boundary (pg. 660) | |
9-5.2 An Example: Distributed Harmonic Force (pg. 662) | |
9-5.3 An Example: Harmonic Force on Boundary (pg. 665) | |
9-6 SUMMARIES (pg. 672) | |
Problems for Chapter 9 (pg. 673) | |
BIBLIOGRAPHY (pg. 684) | |
1 Historical (pg. 684) | |
2 Astronomy (pg. 686) | |
3 Design, Systems, and Modeling (pg. 686) | |
4 Elementary Dynamics (pg. 686) | |
5 Intermediate/Advanced Dynamics (pg. 686) | |
6 Hamilton’s Law of Varying Action and Hamilton’s Principle (pg. 687) | |
7 Electric and Electromechanical Systems (pg. 687) | |
8 Vibration (pg. 687) | |
APPENDIX A: FINITE ROTATION (pg. 688) | |
A-1 CHANGE IN POSITION VECTOR DUE TO FINITE ROTATION (pg. 688) | |
A-2 FINITE ROTATIONS ARE NOT VECTORS (pg. 690) | |
A-3 DO ROTATIONS EVER BEHAVE AS VECTORS? (pg. 692) | |
A-3.1 Infinitesimal Rotations Are Vectors (pg. 692) | |
A-3.2 Consecutive Finite Rotations about a Common Axis Are Vectors (pg. 692) | |
APPENDIX B: GENERAL KINEMATIC ANALYSIS (pg. 694) | |
B-1 ALL ANGULAR VELOCITIES DEFINED WITH RESPECT TO FIXED REFERENCE FRAME (CASE 1) (pg. 694) | |
B-2 EACH ANGULAR VELOCITY DEFINED WITH RESPECT TO IMMEDIATELY PRECEDING FRAME (CASE 2) (pg. 698) | |
APPENDIX C: MOMENTUM PRINCIPLES FOR SYSTEMS OF PARTICLES (pg. 705) | |
C-1 ASSERTED MOMENTUM PRINCIPLES (pg. 705) | |
C-2 PRINCIPLES FOR SINGLE PARTICLE (pg. 706) | |
C-3 PRINCIPLES FOR SYSTEM OF PARTICLES (pg. 707) | |
C-3.1 Asserted System Momentum Principles (pg. 708) | |
C-3.2 System Momentum Principles Derived from Particle Momentum Principles (pg. 709) | |
C-3.3 Conditions on Internal Forces (pg. 711) | |
C-3.4 Relationships between Momentum Principles and Conditions on Internal Forces (pg. 712) | |
C-3.5 Linear Momentum Principle in Terms of Centroidal Motion (pg. 714) | |
C-3.6 Angular Momentum Principle about Arbitrary Point (pg. 715) | |
C-3.7 System of Particle Model in Continuum Limit (pg. 717) | |
C-4 ANGULAR MOMENTUM PRINCIPLE IN NONINERTIAL INTERMEDIATE FRAME (pg. 719) | |
APPENDIX D: ELEMENTARY RESULTS OF THE CALCULUS OF VARIATIONS (pg. 728) | |
D-1 INTRODUCTION (pg. 728) | |
D-2 SUMMARY OF ELEMENTARY RESULTS (pg. 730) | |
D-3 EULER EQUATION: NECESSARY CONDITION FOR A VARIATIONAL INDICATOR TO VANISH (pg. 734) | |
APPENDIX E: SOME FORMULATIONS OF THE PRINCIPLES OF HAMILTON (pg. 737) | |
E-1 MECHANICAL FORMULATIONS (pg. 737) | |
E-1.1 Hamilton’s Law of Varying Action (pg. 740) | |
E-1.2 Hamilton’s Principle (pg. 741) | |
E-1.3 Lagrange’s Equations (pg. 742) | |
E-1.4 Discussion (pg. 743) | |
E-2 HAMILTON’S PRINCIPLE FOR ELECTROMECHANICAL SYSTEMS USING A DISPLACEMENT-CHARGE FORMULATION (pg. 744) | |
E-3 HAMILTON’S PRINCIPLE FOR ELECTROMECHANICAL SYSTEMS USING A DISPLACEMENT-FLUX LINKAGE FORMULATION (pg. 747) | |
E-4 WORK-ENERGY RELATION DERIVED FROM LAGRANGE’S EQUATIONS (pg. 749) | |
APPENDIX F: LAGRANGE’S FORM OF D’ALEMBERT’S PRINCIPLE (pg. 754) | |
F-1 FUNDAMENTAL CONCEPTS AND DERIVATIONS (pg. 754) | |
F-2 EXAMPLES (pg. 757) | |
APPENDIX G: A BRIEF REVIEW OF ELECTROMAGNETIC (EM) THEORY AND APPROXIMATIONS (pg. 763) | |
G-1 MAXWELL’S EQUATIONS: COMPLETE FORM (pg. 763) | |
G-1.1 Integral Form (pg. 763) | |
G-1.2 Differential Form (pg. 765) | |
G-2 MAXWELL’S EQUATIONS: ELECTROSTATICS AND MAGNETOSTATICS (pg. 765) | |
G-3 MAXWELL’S EQUATIONS: ELECTROQUASISTATICS AND MAGNETOQUASISTATICS (pg. 766) | |
G-3.1 Electroquasistatics (pg. 766) | |
G-3.2 Magnetoquasistatics (pg. 768) | |
G-4 ENERGY STORAGE IN ELECTROQUASISTATICS AND MAGNETOQUASISTATICS (pg. 770) | |
G-4.1 Energy Storage in Electroquasistatics (pg. 771) | |
G-4.2 Energy Storage in Magnetoquasistatics (pg. 773) | |
G-5 KIRCHHOFF’S “LAWS” (pg. 774) | |
G-5.1 Kirchhoff’s Current “Law” (pg. 774) | |
G-5.2 Kirchhoff’s Voltage “Law” (pg. 775) | |
G-5.3 Summary (pg. 776) | |
APPENDIX H: COMPLEX NUMBERS AND SOME USEFUL FORMULAS OF COMPLEX VARIABLES AND TRIGONOMETRY (pg. 777) | |
H-1 INTRODUCTION (pg. 777) | |
H-2 ELEMENTARY ALGEBRAIC OPERATIONS OF COMPLEX NUMBERS (pg. 780) | |
H-3 COMPLEX CONJUGATES (pg. 781) | |
H-4 A USEFUL FORMULA OF COMPLEX VARIABLES (pg. 782) | |
H-5 USE OF COMPLEX VARIABLES IN HARMONIC RESPONSE ANALYSES (pg. 787) | |
H-6 USEFUL FORMULAS OF TRIGONOMETRY (pg. 796) | |
APPENDIX I: TEMPORAL FUNCITON FOR SYNCHRONOUS MOTION OF TQO-DEGREE-OF-FREEDOM SYSTEMS (pg. 800) | |
I-1 FREE UNDAMPED EQUATIONS OF MOTION (pg. 800) | |
I-2 SYNHRONUS MOTION (pg. 800) | |
I-3 GENERAL TEMPORAL SOLUTION (pg. 801) | |
I-4 SPECIAL (SEMIDEFINITE) TEMPORAL SOLUTION (pg. 803) | |
I-5 GENERALIZATION TO SYSTEMS HAVING MORE DEGREES OF FREEDOM (pg. 803) | |
APPENDIX J: STABILITY ANALYSES OF NONLINEAR SYSTEMS (pg. 804) | |
J-1 STATE-SPACE STABILITY FORMULATION (pg. 804) | |
J-1.1 State-Space Representation of Equations of Motion (pg. 804) | |
J-1.2 Equilibrium States (pg. 806) | |
J-1.3 Linearization about Equilibrium States (pg. 808) | |
J-1.4 Concept and Types of Stability (pg. 809) | |
J-1.5 Stability of Linearized Systems (pg. 811) | |
J-1.6 Local Stability of Nonlinear Systems (pg. 814) | |
J-1.7 Nonllunear Stability Analyses (pg. 815) | |
J-1.8 Summary of State-Space Stability Analysis (pg. 815) | |
J-2 NONLINEAR STABILITY ANALYSIS FOR CONSERVATIVE SYSTEMS (pg. 816) | |
APPENDIX K: STRAIN ENERGY FUNCTIONS (pg. 822) | |
K-1 CONCEPT (pg. 822) | |
K-2 STRAIN ENERGY DENSITY FUNCTION (pg. 822) | |
K-3 STRAIN ENERGY FUNCTION (pg. 824) | |
K-4 EXAMPLES (pg. 825) | |
ANSWERS TO MOST OF THE ODD-NUMBERED PROBLEMS (pg. 833) | |
LIST OF TABLES (pg. 843) | |
KEY DYNAMICAL PRINCIPLES, FORMULAS, & CONVERSION FACTORS (pg. 846) | |
INDEX (pg. 851) |
James H. Williams Jr.
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