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McLachlan N.W. — Ordinary Non-Lineal Differential Equations in Engineering and Physical Sciences
McLachlan N.W. — Ordinary Non-Lineal Differential Equations in Engineering and Physical Sciences



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Название: Ordinary Non-Lineal Differential Equations in Engineering and Physical Sciences

Автор: McLachlan N.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1950

Количество страниц: 225

Добавлена в каталог: 28.10.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acoustical power transmitted in loudspeaker horn      185
Adiabatic curve, non-linearity due to      1 75 180
Aerodynamical forces, self-oscillation due to      140
Amplitude-frequency curves      59 60
Amplitude-frequency modulation in loudspeaker reproduction      78
Amplitude-frequency relation for nonlinear mass-spring system      57 70
Amplitude-frequency relation for thermionic valve circuit      82
Astronomy, differential equations in      21
Bending length of fabric (the heavy elastica)      175 178 179
Bernoulli's equation      11
cnt (Jacobian elliptic cosine)      26
Combination (sum and difference) tones      78
Coulomb damping      101
Creep in eccentrically loaded columns      171
Curved steel shells, impulse tests of      155
Differences, method of, for solving nonlinear D.E.      166 173
Differential equations, methods of solving non-linear      8
Elastica      34
Elastica, heavy      174
Electrical motor-generator, self-oscillations      47
Electrically maintained tuning fork      90
Elliptic cosine      26
Elliptic cosine, graph of      29
Elliptic function $\wp(u)$      39 40
Elliptic integral      26 36—38
Elliptic sine      26
Energy equality, principle of      104
energy equation      27 55 61
Entrainment (silent zone in valve oscillator)      83
Equivalent linear differential equation      103
Exponential loudspeaker horn, sound waves of finite amplitude in      180
Finite differences, method for solving non-linear D.E.      166 173
Flare in loudspeaker horn, influence of      186
Flexometer for testing fabrics, leather      175
Fourier series solution of non-linear D.E.      29 54
Frequency modulation in loudspeaker reproduction      78
Froude's pendulum      138
Graphical method of solving non-linear D.E.      145
Heart-loop for testing flimsy fabrics      175
Hydro-electric installation, surges in      95
Impulse tests of steel shells      155
Inductive tuning      109
Intermodulation frequencies      75
Isocline method of solving non-linear D.E.      145 158 104
Iteration method of solving non-linear D.E.      48
Jacobian elliptic cosine      26
Jacobian elliptic sine      26
Jump phenomenon      59 70
Linear equivalent of non-linear D.E.      106
Linearization of electrical circuits having non-linear elements      107
Loudspeaker horn, sound waves of finite amplitude in      180
Maclaurin's theorem, used for solving non-linear D.E.      167 177
Mass-spring system, non-linear      17 24 48 52
Mathieu's equation      113
Mathieu's equation, as stability criterion      188
Mathieu's equation, experimental illustration of unstable solution      117 118 120
Mathieu's equation, solution graphs      115 116
Mathieu's equation, stability chart for      114 116
Melde's experiment      120
Negative resistance      136
Non-linear coupling, oscillation due to      141
Non-linear differential equation, definition of      9
Non-linear element in physical system, stabilization due to      119 121 138 139
Non-linear spring control, method of obtaining      25
Numerical solution of non-linear D.E.      168
Parametric excitation of oscillations      6 119 120
Periodic coefficients, differential equations having      113
Perturbation method for solving nonlinear D.E.      43 50
Plane jet in hydrodynamics      20
Principle of energy equality      104
Relaxation oscillations      6 138 151 153
Relaxation oscillations, periodic time of      154
Relaxation oscillations, waveform of      152
Riccati's equation      12
Self-oscillation due to aerodynamical forces      140
Self-oscillation due to aerodynamical forces, solid friction      135
Self-oscillation of motor-generator combination      47
Ship stabilization      92 95
simple pendulum      31
Simple pendulum with oscillating support      131
Simpson's rule, application to numerical solution of non-linear D.E.      169
Slowly varying amplitude and phase, method for solving non-linear D.E.      87
snt (Jacobian elliptic sine)      20
Sound waves of finite amplitude      1
Sound waves of finite amplitude in loudspeaker horn      180
Stability chart for Mathieu's equation      114 116
Stiffness, definition of      24
Subharmonic, higher orders      66
Subharmonic, mechanism exhibiting      130—132
Subharmonic, order 2      70
Subharmonic, order 3      62
Subharmonic, stability of, order 2      72
Subharmonic, stability of, order 3      188
Subharmonics and relaxation oscillations      84 85
Subharmonics in loudspeaker diaphragms      128
Surges in hydro-electric installation      95
Synchronous electrical motor, stability of      160
Thermionic valve oscillator      41 111
Thermionic valve oscillator, silent zone (entrainment)      83
Thermionic valve, transconductance of      41 110
Unstable subharmonics      72 189
Valve, thermionic, oscillatory circuit      41 111
Valve, thermionic, oscillatory circuit, forced oscillation in      80
Valve, thermionic, oscillatory circuit, silent zone      83
Vibrating thread with periodically variable tension      120
Vibrating thread with periodically variable tension, stability of      125
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