An Elementary Treatise on Analytic Mechanics: With Numerous Examples

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D. Van Nostrand, 1884 - 511 σελίδες
 

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Περιεχόμενα

Action and Reaction
9
Geometric Representation of Velocity and Acceleration
10
Kinetic Measure of Force
11
Absolute or Kinetic Unit of Force
13
Three Ways of Measuring Force
14
Meaning of g in Dynamics
15
Action and Reaction
16
Gravitation and Absolute Measure
17
Examples
18
CHAPTER II
21
Three Ways of Measuring Force
22
Composition of Velocities
23
Composition of Forces
24
gestions Several others also of my friends have kindly assisted
25
Three Concurring Forces in Equilibrium
26
The Polygon of Forces
27
Parallelopiped of Forces
28
Resolution of Forces
30
Magnitude and Direction of Resultant
31
Conditions of Equilibrium
32
Resultant of Concurring Forces in Space
34
Equilibrium of Concurring Forces in Space
35
Resultant of Concurring Forces in Space
38
Equilibrium of Concurring Forces on a Smooth Plane
39
Examples
45
Signs of Moments
47
Geometric Representation of a Moment
48
Two Equal and Opposite Parallel Forces
49
Moment of a Couple
50
Effect of a Couple on a Rigid Body
51
Effect of Transferring Couple to Parallel Plane not altered
52
A Couple replaced by another Couple
53
A Force and a Couple
54
Resultant of any number of Couples
55
Resultant of Two Couples
56
CHAPTER III
57
Resultant of Two Parallel Forces
58
Moment of a Force
60
ART Page 47 Signs of Moments
61
Moment of a Couple
62
Effect of a Couple on a Rigid Body
63
Effect of Transferring Couple to Parallel Plane not altered
64
A Force and a Couple
65
Resultant of any number of Couples
66
Resultant of Two Couples
67
Varignons Theorem of Moments
69
Varignons Theorem for Parallel Forces
71
Equilibrium of a Rigid Body under Parallel Forces
74
Equilibrium of a Rigid Body under Forces in any Direction
75
Equilibrium under Three Forces
76
Centre of Parallel Forces
77
Equilibrium of a Rigid Body under Parallel Forces 61 Equilibrium of a Rigid Body under Forces in any Direction 62 Equilibrium under Three Force...
85
Equilibrium of Parallel Forces in Space
87
Equilibrium of Forces acting in any Direction in Space
88
Equilibrium of Forces acting in any Direction in Space Examples
90
CHAPTER IV
100
103 66 Centre of Gravity 67 Planes of SymmetryAxes of Symmetry 68 Body Suspended from a Point
101
Body Supported on a Surface 70 Different kinds of Equilibrium
102
Centre of Gravity of Two Masses
103
Centre of Gravity of a Triangle
104
Centre of Gravity of a Triangular Pyramid
105
Centre of Gravity of a Triangular Pyramid 75 Centre of Gravity of a Cone
106
Centre of Gravity of Frustum of Pyramid
107
Centre of Gravity of Frustum of Pyramid 77 Investigations involving Integration
109
Centre of Gravity of the Arc of a Curve
110
Centre of Gravity of a Plane Area
115
Polar Elements of a Plane Area
118
ART PAGE 81 Double IntegrationPolar Formulæ
120
Double IntegrationRectangular Formulæ 2012
122
Centre of Gravity of a Surface of Revolution
123
Centre of Gravity of any Curved Surface
126
Centre of Gravity of a Solid of Revolution 2017
127
Polar Formulæ
130
Centre of Gravity of any Solid
131
Polar Elements of Mass
133
DefinitionsVelocity
134
Special Methods
136
Theorems of Pappus
138
Examples
140
The Straight Line of Quickest Descent
146
CHAPTER V
149
Laws of Friction
150
Magnitudes of Coefficients of Friction
152
Reaction of a Rough Curve or Surface
153
Friction on an Inclined Plane
154
Friction on a Double Inclined Plane
156
Friction on Two Inclined Planes
159
Friction of a Pivot
160
Examples
162
CHAPTER VI
166
Principle of Virtual Velocities
167
103
169
System of Particles Rigidly Connected
170
Examples
171
Examples
172
ART PAGE 106 Functions of a Machine
177
Mechanical Advantage
178
Simple Machines 109 The Lever
180
109
181
The Common Balance
184
Chief Requisites of a Good Balance
185
Chief Requisites of a Good Balance
186
The Steelyard
188
115
190
Toothed Wheels
192
The Screw 129 Relation between Power and Weight in the Screw
204
129a Pronys Differential Screw
206
Examples
207
THE FUNICULAR POLYGONTHE CATENARYATTRACTION 130 Equilibrium of the Funicular Polygon
216
To Construct the Funicular Polygon
218
Cord Supporting a Load Uniformly Distributed
219
The Common CatenaryIts Equation
221
133a Attraction of a Spherical Shell
226
Examples
228
ART PAGE 184 DefinitionsVelocity
231
Acceleration
233
Relation when the Acceleration is Constant
234
Relation when Acceleration varies as the Time
235
Equations of Motion for Falling Bodies
237
Particle Projected Vertically Upwards
239
Compositions of Velocities
242
Resolution of Velocities
243
Motion on an Inclined Plane
245
Times of Descent down Chords of a Circle
247
The Straight Line of Quickest Descent
248
Examples
249
Remarks on Curvilinear Motion
258
Composition and Resolution of Acceleration
259
Examples
260
Examples
261
Motion of Projectiles in Vacuo
266
The ParameterRangeGreatest HeightHeight of Direc trix
267
Velocity of a Particle at any point of its Path
269
Point at which a Projectile will Strike an Inclined Plane
270
The Elevation that the Particle may pass a Given Point
271
Second Method of Finding Equation of Trajectory
272
Velocity of Discharge of Balls and Shells
274
Angular Velocity and Angular Acceleration
278
Accelerations Along and Perpendicular to Tangent
279
When Acceleration Perpendicular to Radius Vector is zero
281
When Angular Velocity is Constant
282
Examples
284
KINETICS MOTION AND FORCE
289
Remarks on Law I
290
Remarks on Law II
291
Remarks on Law III
294
Two Laws of Motion in the French Treatises
295
Motion under the action of a Variable Repulsive Force
298
Motion under the action of an Attractive Force
299
Two Laws of Motion in the French Treatises
300
Motion in a Resisting Medium
302
Motion in the Air against the Action of Gravity
304
Motion of a Projectile in a Resisting Medium
307
Motion of a Projectile in a Resisting Medium
308
Motion in the Atmosphere under a small Angle of Elevation
312
Examples
313
CENTRAL FORCES ART 180 Definitions 321 181 A Particle under the Action of a Central Attraction
321
The Sectorial Area Swept over by the Radius Vector
325
Orbit when Attraction as the Inverse Square of Distance
329
Velocity of Particle at any Point of its Orbit 184 Orbit when Attraction as the Inverse Square of Distance 185 Suppose the Orbit to be an Ellipse
333
Keplers Laws
335
Examples
338
CHAPTER III
345
To Find the Reaction of the Constraining Curve
348
Point where Particle will leave Constraining Curve
349
191 Point where Particle will leave Constraining Curve 192 Constrained Motion Under Action of Gravity 193 Motion on a Circular Arc in a Vertical ...
350
The Simple Pendulum
352
Relation of Time Length and Force of Gravity 196 Height of Mountain Determined with Pendulum 197 Depth of Mine Determined with Pendulum 1...
353
Height of Mountain Determined with Pendulum
354
Depth of Mine Determined with Pendulum
355
Centripetal and Centrifugal Forces
356
358
358
Centrifugal Force at Different Latitudes
359
The Conical PendulumThe Governor
361
Examples
362
CHAPTER IV
370
Impact or Collision
371
24 irect and Central Impact city of BodiesCoefficient of Restitution 370 371
372
Elasticity of BodiesCoefficient of Restitution
373
ART PAGE
374
Direct Impact of Elastic Bodies
375
Loss of Kinetic Energy in Impact of Bodies
378
Loss of Kinetic Energy in Impact of Bodies
380
Oblique Impact of Two Smooth Spheres
382
Examples
383
CHAPTER V
389
General Case of Work done by a Force
390
Work on an Inclined Plane
391
Examples
393
Horse Power
395
Work of Raising a System of Weights
396
Examples
397
Modulus of a Machine
400
Examples
401
Kinetic and Potential EnergyStored Work
404
Examples
406
Kinetic Energy of a Rigid Body Revolving round an Axis
408
Force of a Blow
411
Work of a Water Fall
412
The Duty of an Engine
414
Work of a Variable Force
415
Examples
417
CHAPTER VI
429
Moments of Imertia relative to Parallel Axes or Planes
432
Moments of Inertia relative to Parallel Axes or Planes
436
Moment of Inertia of a Solid of Revolution
437
Moment of Inertia about Axis Perpendicular to Geometric Axis
438
Moment of Inertia of Warious Solid Bodies
440
Moment of Inertia of a Lamina with respect to any Axis
441

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Δημοφιλή αποσπάσματα

Σελίδα 278 - Change of motion is proportional to the impressed force, and takes place in the direction of the straight line in which the force acts.
Σελίδα 278 - I. Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Σελίδα 13 - If three forces, acting at a point, be represented in magnitude and direction by the sides of a triangle taken in order, they will be in equilibrium.
Σελίδα 473 - The attraction of a uniform spherical surface on an external point is the same as if the whole mass were collected at the centre.
Σελίδα 48 - Moment of a Force. — The moment of a force with respect to a point is the product of the force multiplied by the perpendicular distance from the given point to the direction of the force.
Σελίδα 420 - Steiner. is true for bath a plane laminar body and a thin three-dimensional body, and states that the moment of inertia of a body about any axis is equal to its moment of inertia about a parallel axis through...
Σελίδα 12 - The Parallelogram of Forces. — If two forces acting at a point be represented in magnitude and direction by the adjacent sides of a parallelogram, the resultant...
Σελίδα 317 - A particle is projected from a given point in a given direction and with...
Σελίδα 78 - A beam, 30 feet long, balances itself on a point at one-third of its length from the thicker end ; but when a weight of 10 Ibs. is suspended from the smaller end, the prop must be moved 2 feet towards it, in order to maintain the equilibrium.
Σελίδα 280 - Since forces are measured by the changes of motion they produce, and their directions assigned by the directions in which these changes are produced ; and since the changes of motion of one and the same body are in the directions of, and proportional to, the changes of velocity — a single force, measured by the resultant change of velocity, and in its direction, will be the equivalent of any number of simultaneously acting forces.

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