Elements of Analytical Mechanics

الغلاف الأمامي
J. Wiley & Sons, 1887 - 373 من الصفحات
 

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الصفحات المحددة

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Other units
9
Stresses and Motive Forces ART PAGE 21 Statics and kinetics
10
Measure of the intensity of a motive force
11
Impulsive forces
12
Action of forces on free bodies
13
Representation of a force
14
Rectangular components of a force
15
The parallelogram of forces
17
The resultant of forces with common point of application coplanar forces
18
The parallelopipedon of forces
19
The moment of a force
20
Representation of moments
21
Composition and resolution of moments
22
The parallelopipedon of moments
23
Parallel forces
24
Two parallel forces
25
Two forces whose actionlines are opposite general conclusions for parallel forces
26
The moment of a couple
27
Acceleration due to gravity
30
The centre of gravity the principle of the centre of mass general for mulas for the centre of gravity
31
Determination of the centre of gravity by symmetry
33
Centre of gravity of surfaces general formulas
35
ART PACE 53 Centre of gravity of surfaces of revolution spherical zone and conical surface
41
Centre of gravity of volumes general formulas
42
Volumes of revolution paraboloid and spheroid
43
Centre of gravity of volumes by single integration a pyramid and cone
44
Theorems of Pappus
45
Graphical Statics 58 Introductory
46
The force polygon
47
The properties of the polar polygon
49
triangle polygon circular sector and segment parabola and elliptic quadrant
52
Work and Energy 64 Work done by a force
60
Graphical representation of work
61
Energy denned kinetic and potential energy
62
The law of the conservation of energy
66
The fundamental equation of mechanics reference to coordinate axes
67
Application to a rigid solid
69
Application to a free rigid solid
71
Interpretation of equations of translation and rotation
72
Conditions in cases of constraint
73
Conditions of equilibrium
74
Equations of translation conclusions
75
Illustration of conclusions
76
So Equations of rotation
77
Equations of rotation of a body having a fixed point a fixed right line
78
Independence of the motion of translation and rotation
79
Velocity varies with coordinates of centre of mass
80
Rotation under incessant forces
81
Kinetic ene rgy of translation and rotation
82
Translation under impulsion
83
The inverse problem
85
t constant forces
86
2 Motion due to gravity
87
93 3 The trajectory in vacuo
90
4 The trajectory in air
94
Motion of Rotation 95 Moments of inertia
97
Radius and centre of gyration
98
Principal axes
100
Moment of inertia with reference to a parallel axis through the centre of mass
101
tnn Discussion of the momental ellipsoids of a body
102
Determination of the moments of inertia
104
Moments of inertia tabulated
112
Instantaneous Axis 103 Equations of instantaneous axis
113
Direction of instantaneous axis
114
Resultant axis and plane
115
Angular velocity about a principal axis
116
Position of the invariable plane
117
ART PACE 109 The rolling cone
119
no Discussion of the rolling cone
120
The polhode and herpolhode
122
Permanent axes of rotation
124
Eulers equations of rotation
125
Auxiliary angles
127
The gyroscope
128
Differential equations of motion of the gyroscope
132
Definition of impact compression and restitution
134
Direct and central impact
135
Oblique impact
137
Axis of Spontaneous Rotation 124 Equations of spontaneous axis
138
Conditions for development of spontaneous axis
140
Axis and centre of percussion
141
Reciprocity of the centres of percussion and spontaneous rotation for parallel impacts
142
The normal reaction
144
The theorem of energy applied as in free motion
146
The value of the normal reaction
147
Discussion for concave and convex curves
149
Centrifugal force
150
Change in apparent weight due to earths rotation
152
On an inclined plane
153
Mechanical property of circular arcs
155
On the arc of a cycloid
156
On the arc of a circle
159
Constrained Motion about a Fixed Axil 142 The compound pendulum 160
160
The equivalent simple pendulum
161
Reciprocity of the axes of oscillation and suspension
162
Method by the reversible pendulum
165
Length of the equivalent simple pendulum
166
The British standard of length
167
The conical pendulum
169
a straight rod circular arc circular ring circular plate thin spherical shell thick spherical shell
184
The theorem of Laplace
191
Poissons extension of Laplaces theorem 192
192
Another expression of the same theorem 193
193
Motion of a System of Bodies AIT TAGI 168 Translation of the centre of mass of the system
195
Conservation of the motion of the centre of mass
197
Reference to the solar system
198
Conservation of moments invariable axis and plane
199
Conservation of areas
200
Relative acceleration
201
Differential equations of the relative orbit
202
Central Forces 176 Central force denned
203
Differential equation of the orbit
207
Direct and inverse problem in central forces
208
So Particular cases of the direct problem central force attractive and varying directly as the distance
209
Central force repellent
212
The velocity from infinity at any distance R
215
The velocity at any point of the orbit
216
The anomalies
222
Illustration of the anomalies
224
The Solar System 188 The solar system defined
225
Keplers laws
226
Law of universal gravitation
230
THEORY OF MACHINES Resistances ART PAGE 193 Resistances in machines
234
Coefficient of friction
235
Problems involving friction
237
2 Friction on a trunnion
238
3 Friction on a circular pivot
240
4 Friction on a ring pivot
241
5 Friction of a cord on a cylinder
242
Stiffness of cordage
244
Machine defined
246
Theory of machines
247
Use of flywheel
249
Efficiency
250
Simple Machines 202 Gain and loss of power equation of equilibrium
251
The lever
253
The common balance
255
The wheel and axle
257
The differential wheel and axle
260
The movable pulley
263
The block and fall
264
Other combinations of fixed and movable pulleys
266
The work done in moving a body up a plane
268
The screw
271
The modulus of the screw
273
The cord
275
The differential equations of the funicular curve
276
ART PACK 218 The direction of the resultants of equilibrium forces acting on a cord
277
The ratio of the intensities of these resultants
278
The catenary curve
279
The directrix of the catenary
281
MECHANICS OF FLUIDS Introductory 324 Classification of fluids
283
Pascals principle
284
Fundamental equation of mechanical theory of heat
285
Laws of the gaseous state
286
2 Charles or Gay Lussacs
287
Boyles and Charless laws combined
288
Absolute temperatures
289
Poissons laws
291
Elasticity of volume under Boyles law
293
Transmitted pressure on surface
294
Pressure on plane surface
295
Hydrostatic paradox
297
Graphical construction of centre of pressure
298
Buoyant effort of fluids
299
Position of rest of submerged body
300
Specific gravity
301
Stability of floating bodies
302
Condition of stable equilibrium
304
Metacentre
305
Equation of continuity
308
Solution when the potential and velocity functions are exact differen tials
310
Flow of Perfect Liquids through Vessels 253 General formula for velocity of discharge
311
t Upper surface at constant level
313
255 2 Vessel emptying itself
316
Discharge through small orifice
317
Steady Flow of Fluids 257 Two cases liquids and gases
318
Bernoullis law
319
Uniform flow of liquids
320
Steady flow of gases
321
Equilibrium of Liquids in Motion 261 General formula for surface of uniform pressure
323
Liquid rotating about a vertical axis
324
Equilibrium surface of earth
326
Hydraulics
328
Viscosity
329
Mouthpiece of Borda
331
Cylindrical mouthpiece
332
Divergent mouthpiece
335
The hydraulic gradient
336
Hydraulic machines
338
Water Motors 269 Waterwheels
339
Turbines
341
ArT PACK
344
The centrifugal pump
351
The barometer
357
APPENDIX
363
Gravitythe values of g and L
370

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الصفحة 4 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
الصفحة 97 - Z(mr*), is called the moment of inertia of the body with respect to the axis of suspension. The moment of inertia...
الصفحة 295 - ... equal to the depth of the centre of gravity of the surface below the surface of the fluid.
الصفحة 228 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
الصفحة 167 - The straight line or distance between the centres of the two gold plugs or pins (as mentioned in the First Schedule to this Act) in the bronze bar by this Act declared to be the imperial standard for determining the imperial standard yard measured when the bar is at the temperature...
الصفحة 284 - The thermal capacity or heat capacity of a substance is expressed as the amount of heat required to raise the temperature of a unit weight of the substance one degree.
الصفحة 45 - In pyramids and cones the centre of gravity is in the straight line that joins the vertex with the centre of gravity of the base, and at three-fourths of its length from the vertex, and one-fourth from the base.
الصفحة 24 - Hence the moment of the resultant is equal to the sum of the moments of the two components.
الصفحة 169 - S mom = aJ, in which /is the moment of inertia of the body with respect to the axis of rotation.
الصفحة 367 - ... fills the cube of a hundredth part of the meter. Each unit has its decimal multiples and sub-multiples, that is, weights and measures ten times larger, or ten times smaller, than the principal units. The prefixes denoting multiples are derived from the Greek, and are: Deka, ten; hecto, hundred; kilo, thousand, and myria, ten thousand.

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