Engineering Dynamics

by O'Reilly, Oliver M.

• ISBN13: 9780387951454
• ISBN10: 0387951458
• Format: Paperback
• Copyright: 2001-01-01
• Publisher: Springer Verlag

Summary

This primer is intended to provide the theoretical background for the standard undergraduate, mechanical engineering course in dynamics. It grew out of the author's desire to provide an affordable compliment to the standard texts on the subject in which the gap between the theory presented and the problems to be solved is oftentimes too large. The book contains several worked examples and at the end of each chapters summaries and exercises to aid the student in their understanding of the chapter. Teachers who wish to have a source of more detailed theory for the course, as well as graduate students who need a refresher course on undergraduate dynamics when preparing for certain first year graduate school examinations, and students taking the course will find the work very helpful.

Table of Contents

Preface	vii
Elementary Particle Dynamics	1	(10)
Kinematics of a Particle	1	(2)
A Circular Motion	3	(1)
Rectilinear Motions	4	(2)
Given Acceleration as a Function of Time	5	(1)
Given Acceleration as a Function of Speed	5	(1)
Given Acceleration as a Function of Placement	5	(1)
Kinetics of a Particle	6	(1)
Action and Reaction	6	(1)
The Four Steps	6	(1)
A Particle Under the Influence of Gravity	7	(1)
Kinematics	7	(1)
Forces	7	(1)
Balance Law	8	(1)
Analysis	8	(1)
Summary	8	(1)
Exercises	9	(2)
Particles and Cylindrical Polar Coordinates	11	(8)
The Cylindrical Polar Coordinate System	11	(2)
Velocity and Acceleration Vectors	13	(1)
Common Errors	13	(1)
Kinetics of a Particle	14	(1)
The Planar Pendulum	14	(2)
Kinematics	15	(1)
Forces	15	(1)
Balance Law	16	(1)
Analysis	16	(1)
Summary	16	(1)
Exercises	17	(2)
Particles and Space Curves	19	(22)
The Serret-Frenet Triad	19	(3)
The Serret-Frenet Formulae	22	(1)
Examples of Space Curves	23	(8)
A Curve on a Plane	23	(3)
A Space Curve Parametrized by x	26	(1)
A Circle on a Plane	27	(2)
A Circular Helix	29	(2)
Application to Particle Mechanics	31	(2)
A Particle Moving on a Fixed Curve Under Gravity	33	(3)
Kinematics	33	(1)
Forces	34	(1)
Balance Law	35	(1)
Analysis	35	(1)
Summary	36	(1)
Exercises	37	(4)
Friction Forces and Spring Forces	41	(16)
An Experiment on Friction	41	(2)
Static and Dynamic Coulomb Friction Forces	43	(3)
A Particle on a Surface	44	(1)
A Particle on a Space Curve	45	(1)
Some Comments on Friction Forces	46	(1)
A Particle on a Rough Moving Plane	47	(1)
Hooke's Law and Linear Springs	48	(2)
A Particle on a Rough Spinning Cone	50	(3)
Kinematics	51	(1)
Forces	51	(1)
Balance Law	52	(1)
Analysis	52	(1)
Summary	53	(1)
Exercises	54	(3)
Power, Work, and Energy	57	(16)
The Power of a Force	57	(2)
The Work-Energy Theorem	59	(1)
Conservative Forces	60	(1)
Examples of Conservative Forces	61	(2)
Constant Forces	61	(1)
Spring Forces	62	(1)
Energy Conservation	63	(2)
A Particle Moving on a Rough Curve	65	(3)
Kinematics	66	(1)
Forces	66	(1)
Work Done by Friction	66	(1)
The Smooth Curve	67	(1)
Further Examples of Energy Conservation	68	(1)
A Particle in a Conservative Force Field	68	(1)
A Particle on a Fixed Smooth Surface	68	(1)
The Planar Pendulum	69	(1)
Summary	69	(1)
Exercises	70	(3)
Momenta, Impulses, and Collisions	73	(18)
Linear Momentum and Its Conservation	73	(1)
Linear Impulse and Linear Momentum	73	(1)
Conservation of Linear Momentum	74	(1)
Example	74	(1)
Angular Momentum and Its Conservation	74	(4)
Angular Momentum Theorem	75	(1)
Conservation of Angular Momentum	75	(1)
Central Force Problems	76	(1)
Kepler's Problem	76	(1)
A Particle on a Smooth Cone	77	(1)
Collision of Particles	78	(6)
The Model and Impact Stages	79	(1)
Linear Impulses During Impact	80	(1)
Linear Momenta	81	(1)
The Postimpact Velocities	82	(1)
Kinetic Energy and the Coefficient of Restitution	83	(1)
Negative Values of the Coefficient of Restitution	84	(1)
Impact of a Particle and a Massive Object	84	(1)
Collision of Two Spheres	85	(1)
Summary	86	(2)
Exercises	88	(3)
Systems of Particles	91	(16)
Preliminaries	91	(1)
Center of Mass, Momenta, and Kinetic Energy	92	(3)
The Center of Mass	92	(1)
Linear Momentum	93	(1)
Angular Momentum	93	(1)
Kinetic Energy	94	(1)
Kinetics of Systems of Particles	95	(1)
Conservation of Linear Momentum	95	(3)
The Cart and the Pendulum	95	(3)
Conservation of Angular Momentum	98	(4)
Four Whirling Particles	100	(2)
Work, Energy, and Conservative Forces	102	(2)
The Cart and the Pendulum	102	(1)
Four Whirling Particles	103	(1)
Comment	104	(1)
Summary	104	(1)
Exercises	105	(2)
Planar Kinematics of Rigid Bodies	107	(28)
The Motion of a Rigid Body	107	(5)
General Considerations	107	(1)
A Rigid Body	108	(2)
Angular Velocity and Acceleration Vectors	110	(1)
Fixed-Axis Rotation	111	(1)
Kinematical Relations and a Corotational Basis	112	(4)
The Corotational Basis	112	(1)
The Corotational Basis for the Fixed-Axis Case	113	(2)
A Particle Moving on a Rigid Body	115	(1)
Mechanisms	116	(2)
Center of Mass and Linear Momentum	118	(3)
The Center of Mass	119	(1)
The Linear Momentum	120	(1)
Kinematics of Rolling and Sliding	121	(1)
Kinematics of a Rolling Circular Disk	122	(3)
A Common Error	124	(1)
The Sliding Disk	125	(1)
Angular Momenta	125	(1)
Inertia Tensors	126	(4)
Where the Inertia Tensor Comes From	127	(1)
Angular Momentum and the Inertia Tensor	128	(1)
A Circular Cylinder	129	(1)
The Parallel-Axis Theorem	130	(1)
Some Comments on Integrals and Derivatives	130	(2)
Summary	132	(1)
Exercises	133	(2)
Kinetics of a Rigid Body	135	(30)
Balance Laws for a Rigid Body	135	(4)
Resultant Forces and Moments	136	(1)
Euler's Laws	137	(1)
The Fixed-Axis of Rotation Case	138	(1)
The Four Steps	139	(1)
Work-Energy Theorem and Energy Conservation	139	(3)
Koenig's Decomposition	140	(1)
The Work-Energy Theorem	141	(1)
An Alternative Form of the Work-Energy Theorem	142	(1)
Purely Translational Motion of a Rigid Body	142	(5)
The Overturning Cart	143	(4)
A Rigid Body with a Fixed Point	147	(4)
Kinematics	148	(1)
Forces and Moments	149	(1)
Balance Laws	150	(1)
Analysis	150	(1)
Rolling and Sliding Rigid Bodies	151	(2)
Friction	152	(1)
Energy Considerations	153	(1)
Examples of Rolling and Sliding Rigid Bodies	153	(4)
General Considerations	153	(2)
The Rolling Case	155	(1)
The Static Friction Criterion and Rolling	156	(1)
The Sliding Case	157	(1)
An Imbalanced Rotor	157	(3)
Kinematics	158	(1)
Forces and Moments	159	(1)
Balance Laws	160	(1)
Analysis	160	(1)
Summary	160	(2)
Exercises	162	(3)
Systems of Particles and Rigid Bodies	165	(16)
A System of Particles and Rigid Bodies	165	(6)
Momenta and Kinetic Energy	166	(1)
Impulses, Momenta, and Balance Laws	167	(2)
Conservations	169	(2)
An Example of Two Rigid Bodies	171	(4)
Kinematics	171	(1)
Forces and Moments	172	(1)
Balance Laws and Analysis	173	(1)
A Related Example	174	(1)
Impact of a Particle and a Rigid Body	175	(1)
Beyond this Primer	176	(1)
Summary	177	(1)
Exercises	178	(3)
A Preliminaries on Vectors and Calculus	181	(6)
A.1 Vector Notation	181	(1)
A.2 Dot and Cross Products	182	(1)
A.3 Differentiation of Vectors	183	(1)
A.4 A Ubiquitous Example of Vector Differentiation	183	(1)
A.5 Ordinary Differential Equations	184	(3)
A.5.1 The Planar Pendulum	185	(1)
A.5.2 The Projectile Problem	185	(1)
A.5.3 The Harmonic Oscillator	185	(1)
A.5.4 A Particle in a Whirling Tube	186	(1)
B Weekly Course Content and Notation in Other Texts	187	(6)
B.1 Weekly Course Content	187	(4)
B.2 Notation in Other Texts	191	(2)
References	193	(6)
Index	199