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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Slater J.C., Frank N.H. — Mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Admittance 31 33
Alpha particle, scattering of 65
Angles, Euler’s 104 107—120
Angular momentum of rotating rigid body 92—120
Angular rotation, lack of vector character of 102—104
Anharmonic oscillator 40 42
Approximate solution for nonuniform string 183—186
Archimedes’ Principle 230 236
Aristotle 1
Artificial electric line, analogy to weighted string 151 178
Associated Legendre polynomials, or associated spherical harmonics 205
Atwood’s machine 86
Axis of rotation, instantaneous 95—96
Beats 35 168
Bent beam 222
Bernoulli’s equation 232—233
Bessel’s equation and function 181 200—204 240—241 251—252 288 289
Body forces in hydrodynamics 230
Body forces, in elasticity 206
Boundary conditions, for circular membrane 200—204
Boundary conditions, for rectangular membrane 197
Boundary conditions, for string 148 175 185—186
Center of mass 91
Central field, motion in 52—68
Centrifugal force 57
Circular membrane 199—204
Coefficients, of Fourier series 150 279 284
Coefficients, of viscosity 233
Combination tones 42
Complex exponentials and complex, numbers 26 255—257
Compressibility of elastic solid 214
Conductance 31
Conservation of energy 13—16 46—52 77
Conservative system, condition for 13 46—52
Constraints 70 79
Continuity, equation of 226—227
Continuous medium 206—237
Convergence, of Fourier series 281
Convergence, of power series 244—250
Coordinates, curvilinear, vector operations in 285—287
Copernicus 1
Coriolis force 56
Coulomb’s law 53—54
Coupled systems 122—140
Curl, in curvilinear coordinates 286
Curl, of a vector 148 231—232 266
Curvilinear coordinates 285—287
Damping of vibrating string 160—161
Damping, critical 25
Damping, logarithmic 27
Decrement, logarithmic 27 29
Deformation of elastic solid 211—215
Degeneracy, in circular membrane 202
Degeneracy, in coupled oscillators 135—136
Degeneracy, in square membrane 204
Degrees of freedom 70
Determinant 127 275
Difference equations 239—242
Differential analyzer 8 294
Differential equations, general properties of 6
Differential equations, linear, properties of 7 24 33 34
Differential equations, numerical solution of 8 239—242
Direction cosines 259
Discontinuities in functions, Fourier representation of 281
dispersion 23 167—169
Divergence of a vector 226—227
Divergence theorem 267—269
Divergence, in curvilinear coordinates 286
Double Fourier series 199
Double pendulum 141
Eccentricity of conic section 58
Elastic constants 213—223
Elastic solid 206—223
Elastic waves 217—222
Electric circuit 4 27—29
Electric circuit, oscillations of 27—29
Electromagnetic theory 2 6 15 22—23
ellipse 58—62
Ellipsoid, energy 132—133
Energy 7 9—16 38—40 46—52 57 62—66
Equation, in normal coordinates 160
Equation, mechanical, generalized coordinates 69—79
Equation, of continuity 226 227
Equation, of fluid, ideal 229—233
Equation, of membrane 195—196
Equation, of motion of elastic solid 217—219
Equation, of rigid body 90—95 105 109—112
Equation, of string 146
Equation, variable 181
Equation, viscous 233—235
Equations, difference 239—242
Equilibrium, stable 13
Equinoxes, precession of 120—121
Equipotential surfaces 50—51
Euler’s angles 104 107—120
Euler’s equations for rigid body 105 111
Euler’s equations of hydrodynamics 229—233
Even functions 282—283
Expansion in normal functions for variable string 186—188
Expansion, Fourier 21 144 150 279 284
Exponential solution of vibrating particle 25—36
Exponential solution of vibrating rectangular membrane 196—198
Exponential solution of vibrating string 147—149
Exponential string 182—183
Exponential, complex 255—257
External forces generalized coordinates of 71—77
External forces on coupled oscillators 137—140
Falling body 7 10—11
Field, central 52—68
Filter, weighted string as 170
Flow of fluids 224—236
Flow, lines of 224—229
Fluids, flow of 224—236
Flux 225—229
Force, external (see External forces)
Force, generalized 73
Forced vibrations, of coupled oscillators 137—140
Forced vibrations, of particle 21 29—38
Forced vibrations, of string 161
Fourier series 21 144 150 279—284
Fourier series, double 199
Function space 159 189
Functions, odd and even 282—283
Functions, power-series representation of 243 254
Galileo 1
Gauss’s theorem 267—269
Generalized coordinates, equations of motion in 70—88
Generalized coordinates, vector operations in 285—287
Generalized force 73
Generalized force in vibrating string problem 160
Generalized momentum 71—78
Geophysical problems with elastic waves 219—220
Gradient, in curvilinear coordinates 285
Gradient, of a scalar 48 265—266
Gravitational constant 53
Group velocity 168—169
Half width of resonance band 32
Hamiltonian function 174—179
Hamilton’s equations of motion 74—79
Harmonics 149—162 165
Hooke’s law 21 24 211—223
Hooke’s law, modified for viscous fluids 233—234
Huygens 1
Hydrostatic pressure 208 230
Hyperbola 58—62
Ideal fluid 229 233
Impedance 31
Inertia, moment and products of 96—97
Infinite series 243—254
Initial conditions, for circular membrane 202—204
| Initial conditions, for rectangular membrane 198—199
Initial conditions, for string 149 150
Initial conditions, for transient vibrations of particle 25—27
Instantaneous axis 95
Integral, line 46 49 269
Inverse-square law 58—66
Irrotational flow 228—229 232—233
Kepler’s laws 1 60—61
kinetic energy 9—16 71—75 126
Kinetic energy of rigid bodies 97 101
Lagrange, hydrodynamic equation of 231—232
Lagrange’s equations 69—88
Lagrange’s equations for coupled particles 133—134
Lagrange’s equations for rotating body 109—120
Lagrange’s equations for weighted string 160
Lagrangian function 74
Lagrangian function with magnetic field 87
Lagrangian function with relativity 88
Laplace’s equation, for velocity potential 229 232
Laplacian 195 266—267
Laplacian in curvilinear coordinates 286
Larmor precession 121
Legendre polynomials, associated 205
Legendre’s equation 205
Line integrals 46—49 269
Linear differential equation, properties of 24 33 34
Linear restoring force 21—42
Lines of flow 224—229
Lines of force 50
Liquids, flow of 224—236
Lissajous figures 137
Longitudinal waves in elastic solid 219
Membrane, vibrations of 193—205
Moment of inertia 56 96—97
Momentum of jet 5
Momentum, angular 56 73
Momentum, generalized 71—78
Motion in several dimensions 43—68
Motion of rigid bodies 89—121
Motion of several particles 90—94 122—142
Motion, Newton’s law of 2 4 44 69 71—73 92 218
Neumann functions 201 252 288—289
Newton 1 (see also Motion)
Nodal line, Euler’s angles 108
Nodes in vibrating membrane 202
Nonconservative systems 46
Nonuniform string 180—192
Normal coordinates 122—140 156—161
Normal functions for vibrating string 149—162
Normal modes 127—140 149—162 185- 188
Normal stresses 208 296
Normalization, of coupled systems 129—130
Normalization, of nonuniform string 187
Normalization, of weighted string 157
Numerical integration 8 239—242
Nutation 86 120
Odd functions 282—283
Orbits, central motion of 58—66
Orthogonality 262—264 275—276
Orthogonality of Bessel's functions 204
Orthogonality of coupled systems 129—130
Orthogonality of nonuniform string 186—187
Orthogonality of sine and cosine 144 150 159
Orthogonality of weighted string 157
Oscillations, of electric circuit 23—24 30—31
Oscillations, simple harmonic 21—24
Oscillator, anharmonic 40 42
Oscillator, coupled 122—140
Oscillator, linear 21—42
Oscillator, nonlinear 40 42
Overtone 149—162 185—188
Pendulum, spherical 79—86
Perturbation theory of nonuniform string 188—190
Plane waves, elastic 218—221
Planetary motion 58—66
Poiseuille’s law 233—235
Poisson’s ratio 216 222
Pole of function 245
Polynomials, Legendre’s 205
potential energy 9—16 62—66
Potential, velocity 228—229
Power series 8 243—255
Power-series solution for differential equations 243—254
Precession 112—120
Pressure, in elasticity 208
Pressure, in hydrodynamics 230
Principal axes, of coupled systems 130
Principal axes, of inertia 98—105
Principal axes, of stress 209—211
Products, of inertia 97
Products, of vectors 259—261
Progressive waves 163—170
q 27—38 139 176
Quantum theory 3 23 64—65 77 278
Radial motion in central field 57 62 64
Reactance 31
Rectangular membrane 196—199
Reflection, of elastic waves 219—220
Reflection, of waves on strings 170—177
Relativity, theory of 5 19
Resistance 31
Resonance 22 29—38 138—139 176
Rest mass 5
Rigid bodies 89—121
Rolling-ball analogy 13
Rotating system of axes, vector in 95
Rotation of coordinates 261—264 277
Rumford 14
Rutherford 65
Scalar product 260
Secular equation, for coupled oscillators 128 152
Secular equation, for perturbation theory 189—190
Separation of variables, method of 147 194—202
Series, Fourier 21 144 150 279—284
Series, power 8 243—255
Several particles, general problem of motion of 90—94 122—142
Shearing stress and strain 208—211
Simple harmonic vibrations 21—42
Singularity of function 245
Solids, elastic 206—223
Sources and sinks 226—227
Spherical harmonics 205
Spherical pendulum 79—86
Square membrane, degeneracy of 204
Stable equilibrium 13
standing waves 149 170—177
Statistical mechanics 78
Steady flow of fluids 227
Stokes’s theorem 48 269—271
Strains in elastic solid 211—223
Streamlines 226—229
Stresses in elastic solid 206—223
String, vibrations of 143 192
Sturm — Liouville equation 188
Superposition of transient and forced motion 33—38
Surface forces 206—223
Susceptance 31
Symmetrical top 107—120
Symmetry of stress tensor 210
Taylor’s 243—252
Tensors 96—97 207—223 272-278
Top, precession of 115—120
torque 56 73 98
Torque, due to shearing stress 210
Torque-free motion of symmetrical rigid body 112—115
Transients 21 33—38
Transients, initial conditions for 34 35
Transverse waves in elastic solid 219
Traveling waves 148
Tubes of flow 225 229
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