Seely F.B. Analytical Mechanics for Engineers
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PREFACE
V
The authors
wish to
acknowledge
their
indebtedness to
Pro-
fessor
A. N. Talbot for his interest
in
the book
during
its
prepara-
tion
and
for his
helpful suggestions
on
the
treatment of
certain
important topics.
The authors
are also
indebted
to
Professor
G.
A.
Goodenough
for valuable
material
in
the treatment
of
Gov-
ernors and to
Professor 0. A. Leutwiler for
the
data and
figures
for a
number of valuable
engineering problems.
F. B.
S.
N. E. E.
URBANA, ILLINOIS,
December,
1920.
CONTENTS
PAGE
Preface..
.
iii
PART
I.
STATICS
CHAPTER
I. FUNDAMENTAL CONCEPTIONS AND
DEFINITIONS
1.
Introduction
1
2.
RigidBody
3
3.
Conception
of
a
Force
3
4.
External Effects
of
a Force
. 4
5.
Characteristics of a
Force
4
6.
Measure of a Force.
Units
4
7. Scalar
and Vector
Quantities.
Vector
Representation
of
a Force
...
6
8. Classification
of Forces. Definitions
7
9.
Principle
of
Transmissibility
8
10.
Parallelogram
Law
8
11.
Triangle
Law
9
12. Resolution of
a
Force
11
13.
Moment of
a
Force 14
14.
Principle
of Moments.
Varignon's
Theorem
16
15.
Couples
19
16.
Characteristics of
a
Couple
20
17.
Vector
Representation
of
a
Couple
20
18. Resolution of
a Force into a Force and a
Couple
22
19.
Methods
of
Solution of Problems..
,
24
CHAPTER
II. RESULTANTS
OF FORCE
SYSTEMS
20. Introduction
28
1.
Collinear
Forces
21.
Algebraic
Method
28
2. Concurrent Forces in
a Plane
22.
Graphical
Methods
29
23.
Algebraic
Method
31
vii
viii
CONTENTS
3.
Parallel Forces in a
Plane
PAGE
24.
Graphical
Methods
34
25.
Principle
of Moments
38
26.
Algebraic
Method
40
27.
Couples
44
4.
Non-concurrent, Non-parallel
Forces
in
a Plane
28.
Graphical
Methods
48
29.
Principle
of Moments
49
30.
Algebraic
Method
50
5.
Concurrent Forces in
Space
31.
Graphical
Method
53
32.
Algebraic
Method
54
6. Parallel Forces
in
Space
33.
Graphical
Method
56
34.
Principle
of Moments
57
35.
Algebraic
Method
57
7.
Couples
in
Space
36.
Resultant of
a
System
of
Couples
60
37.
Composition
of
Couples by
Means of Vectors
62
38.
Resolution
of
Couples
64
8.
Non-concurrent, Non-parallel
Forces
in
Space
39.
Graphical
Method
65
40.
Principle
of Moments
65
41.
Algebraic
Method
66
CHAPTER
III.
EQUILIBRIUM
OF FORCE SYSTEMS
1.
Introduction
42.
Preliminary
69
43.
Graphical
Conditions
of
Equilibrium
70
44.
Algebraic
Conditions of
Equilibrium
70
2. Collinear Forces
45.
Equations
of
Equilibrium
72
3.
Concurrent Forces
in
a
Plane
46.
Equations
of
Equilibrium
73
47 Lami's
Theorem
74
48
Three
Forces in
Equilibrium
75
4.
Parallel Forces
in a
Plane
49.
Equations
of
Equilibrium
78
CONTENTS
ix
5.
Non-concurrent,
Non-parallel
Forces in
a
Plane
PAGE
50.
Equations
of
Equilibrium
82
51.
Graphical
Solution
of a
Typical
Problem
85
52.
Choice
of Moment-centers
and of
Directions
of
Resolution 87
6.
Equilibrium
of
Trusses,
Cranes,
and Cables
53.
Stresses
in
Trusses
88
54.
Method
of Joints
89
55.
Method
of
Sections
90
56.
Graphical
Analysis
of
Trusses 95
57.
Cranes
98
58.
Stresses
in Flexible
Cables
102
59.
The Parabolic
Cable ,
. 102
60.
The
Catenary
106
7. Concurrent
Forces
in
Space
61.
Equations
of
Equilibrium
110
8.
Parallel
Forces
in
Space
62.
Equations
of
Equilibrium
,
112
9.
Non-concurrent, Non-parallel
Forces
in
Space
63.
Equations
of
Equilibrium
114
CHAPTER IV.
FRICTION
64.
Friction
Defined
127
65.
Coefficient
of Friction
128
66.
Angle
of
Friction and
the Friction
Cone
129
67.
Angle
of
Repose
133
68.
The Laws
of Friction
134
69.
The
Inclined
Plane
135
70.
The
Wedge
138
71.
The
Screw
142
72.
Journal
Friction and
the
Friction Circle
145
73.
Pivot
Friction
. 148
74.
Solid Flat
Pivot
149
75.
Hollow
Flat Pivot
or Collar
Bearing
150
76. Conical Pivot
151
77.
Rolling
Resistance
153
78 Belt
Friction
155
CHAPTER
V.
FIRST
MOMENTS
AND
CENTROIDS
79.
First
Moments
160
80.
Centroids
160
81 . Planes
and
Lines of
Symmetry
162
82. Centroids
by
Integration
163
X
CONTENTS
PAGffl
83.
Centroids of
Composite Figures
and Bodies
168
84. Theorems
of
Pappus
and Guldinus
171
85. Center of
Gravity
and
Mass-center
173.
86.
Graphical
Method
of
Determining
Centroids of
Areas
177
87. Determination of Center
of
Gravity by
Experiment
178
CHAPTER
VI. SECOND
MOMENT.
MOMENT
OF
INERTIA
1.
Moments
of
Inertia
of
Areas
88. Moment of
Inertia of
an Area Defined
180
89. Polar Moment of
Inertia
181
90. Radius of
Gyration
182
91. Parallel Axis
Theorem for
Areas
183
92.
Moments of
Inertia
by
Integration
184
93.
Moments
of Inertia of
Composite
Areas
190
94. Product of
Inertia Defined
194
95. Axes of
Symmetry
194
96. Parallel Axis
Theorem
for
Products of
Inertia
196
97.
Moments of
Inertia
with
Respect
to
Inclined
Axes
198
98.
Principal
Axes
199
99.
Moments of
Inertia
of
Areas
by
Graphical
and
Approximate
Methods 202
2.
Moments
of
Inertia
of
Bodies
100. Moment of
Inertia of Mass Defined
205
101.
Radius of
Gyration
207
102. ParaUel
Axis Theorem
for Masses
207
103.
Moments of
Inertia with
Respect
to
Two
Perpendicular
Planes
208
104.
Moments of
Inertia
of
Simple
Solids
by Integration
209
105. Moments
of Inertia of
Composite
Bodies
2J8
106.
Moments
of
Inertia
of
Bodies
by
Experimental
Methods
220
PART
II.
KINEMATICS
107.
Introduction
221
CHAPTER
VII. MOTION
OF A
PARTICLE
108.
Types
of
Motion
222
109. Linear
Displacement
222
110.
Angular
Displacement
224
111.
Relation
between
Linear and
Angular Displacements
225
112.
Linear
Velocity
and
Speed
226
113.
Distance-time
Graph
228
114.
Angular
Velocity
229
115.
Relation
between Linear
and
Angular
Velocities 230
116.
Components
of
Velocity
231
CONTENTS
xi
PAGE
117.
Linear
Acceleration
v.
235
118.
Tangential
and
Normal Accelerations
236
119.
Speed-time
Graph
241
120.
Angular
Acceleration
242
12,1.
Relation between
Linear
and
Angular
Accelerations:
243
122.
Axial
Components
of Acceleration 245
123.
Motion
of
a
Projectile
248
124.
Uniformly
Accelerated
Rectilinear
Motion 250
125.
Uniformly
Accelerated
Circular
Motion 251
>
{
126.
Simple
Harmonic
Motion
253
Il27.
Non-uniformly
Accelerated
Motion 256
128.
Relative
Motion
262
129. Transverse
and
Radial
Components
of Acceleration 269
130.
Coriolis'
Law
270
CHAPTER
VIII.
MOTION
OF
RIGID BODIES
131.
Introduction
276
132. Translation
276
133.
Rotation
277
'
134.
Plane
Motion
278
135.
Instantaneous
Center.
284
PART
III.
KINETICS
CHAPTER
IX.
FORCE, MASS,
AND
ACCELERATION
1.
Preliminary
Considerations.
Kinetics
of
a
Particle
136. Introduction
287
137.
The
General
Kinetics
Problem
288
138.
Characteristics
of a
Force
System
288
139.
Inertia and
Mass
289
140.
Newton's
Laws
293
141.
Mathematical
Statement
of Newton's
Second
Law.
Units
294
142.
Other
Systems
of Units
296
143.
Equations
of
Motion
for
a Particle
297
2.
Kinetics
of
Bodies
144.
T
ntroduction.
Methods
of
Analysis
303
Translation
145.
Kinetics
of a
Translating
Rigid
Body
305
Rotation
146.
Kinetics of a
Rotating Rigid Body
313
147. Second
Method
of
Analysis.
Inertia Forces
325
148. Center
of Percussion
.
.
.
336
xii
CONTENTS
Plane Motion
PAGE
149. Kinetics of Plane Motion of a
Rigid
Body
336
150. Second Method
of
Analysis.
Inertia Forces
345
151. Limitations
of the Moment
Equation,
T
=
Ia
351
152.
Principle
of the Motion of the
Mass-center
353
3.
Special
Topics
in
Kinetics
153. Introduction
356
154.
Hoop
Tension in
Flywheels
356
155.
Superelevation
of
Railway
Track
358
Pendulums
156.
Simple
Circular
Pendulum
360
157.
Compound
Pendulum
363
158.
Center of Oscillation
364
159.
Torsion Pendulum
365
160.
Experimental
Determination
of
Moment
of Inertia
367
Balancing
161. Need
for
Balancing
369
162.
Balancing
of
Rotating
Masses
370
163. Several Masses in a
Single
Plane
of
Rotation
372
164.
Masses
in
Different Transverse Planes
373
The
Gyroscope
165.
The Problem Defined
378
166.
Analysis
of
Forces
in the
Gyroscope
379
167. The Moment of
the
Gyroscopic
Couple
382
Governors
168.
The
Action
of
Governors
386
169. The Conical
Pendulum
387
170. The
Loaded
Governor
388
171.
The Porter
Governor
389
172.
The
Centrifugal
Shaft
Governor
391
173. The
Inertia Shaft
Governor
392
174.
Comparison
of
the Two
Types
of Governors 393
175.
Analysis
of Forces in
the Rite's
Inertia Governor 393
CHAPTER X. WORK AND
ENERGY
176. Introduction
405
1. Work and Power
177. Work
Defined
406
178.
Algebraic
Expressions
for Work Done
by
a Force 406
179.
Work
Done
by
a
Couple
408
180. Work
a Scalar
Quantity.
Sign
and
Units of Work
409
181.
Graphical
Representation
and Calculation of Work
409
CONTENTS xiii
_
PAGE
182.
Work
Done on
a
Body
by
a Force
System
4~I4
183.
Power
Denned 417
184.
Units
of Power
417
185.
Special Equations
for
Power 418
2.
Energy
186.
Energy
Defined
420
187.
Potential
Energy
421
188.
Kinetic
Energy
422
189.
Kinetic
Energy
of a
Particle 422
190.
Kinetic
Energy
of a
Body
424
191.
Non-mechanical
Energy
428
3.
Principles
of
Work
and
Energy
192.
Preliminary
430
193.
Principle
of Work and Kinetic
Energy
430
194.
Application
of
Principle
to
Special
Cases of
Motion of
Rigid
Bodies. 432
195. Conservation
of
Energy
439
196.
Relation
between
Potential and
Kinetic
Energy
for
Conservative
Systems
440
4.
Efficiency. Dissipation of
Energy
197.
Efficiency
Defined
442
198.
Dissipation
of
Energy
443
199. Work
Lost
Due to Friction
in
Bearings
444
200.
A
Simple Dynamometer.
Prony
Brake 446
CHAPTER XI.
IMPULSE AND MOMENTUM
201.
Preliminary
449
1.
Impulse
202.
Impulse
and
Impact
Defined.
Units
450
203.
Components
of Linear
Impulse
451
204.
Moment of
Impulse.
Angular Impulse
452
2. Momentum
205. Momentum
of a Particle Defined. Units
453
206.
Components
of Momentum. Moment of
Momentum
454
207.
Linear
Momentum
of a
Body
455
208.
Angular
Momentum
of a
Rotating Rigid Body
456
209.
Angular
Momentum of
a
Rigid
Body Having
Plane
Motion
457
3.
Principles of
Impulse
and Momentum
210.
Preliminary
459
211.
Principle
of
Linear
Impulse
and
Linear Momentum
459
212.
Principle
of
Angular Impulse
and
Angular
Momentum
461
xiv
CONTENTS
213.
Method of
Analysis
of
the
Motion
of
a
Body
by
Means
of
Impulse
and
Momentum
462
214.
Application
of
the
Principles
of
Impulse
and
Momentum
to
Special
Types
of
Motion of
Rigid
Bodies
463
215. Conservation
of Momentum
467
216.
Impact
471
217.
Impact
of Two
Translating
Bodies
. .
473
218.
Impact
of a
Translating
Body
with a
Rotating
Body
475
219. Loss
of Kinetic
Energy
in Direct Central
Impact
476
220.
Angular
Momentum a Vector
Quantity
477
221.
The
Gyroscopic
Couple
478