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Lanczos C. — Variational principles of mechanics
Lanczos C. — Variational principles of mechanics

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Название: Variational principles of mechanics

Автор: Lanczos C.

Аннотация:

For a number of years the author has conducted a two-semester lecture course on the variational principles of mechanics at the Graduate School of Purdue University. Again and again he experienced the extraordinary elation of mind which accompanies a preoccupation with the basic principles and methods of analytical mechanics. There is hardly any other branch of the mathematical sciences in which abstract mathematical speculation and concrete physical evidence go so beautifully together and complement each other so perfectly. It is no accident that the principles of mechanics had the greatest fascination for many of the outstanding figures of mathematics and physics. Nor is it an accident that the European universities of earlier days included a course in theoretical mechanics in the study plan of every prospective mathematician and physicist. Analytical mechanics is much more than an efficient tool for the solution of dynamical problems that we encounter in physics and engineering. However great may be the importance of the gyroscope as a practical instrument of navigation or engineering, it is not needed as an excuse to demonstrate the importance of theoretical mechanics. The very existence of the general principles of mechanics is their justification.


Язык: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 327

Добавлена в каталог: 23.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
action      5
Action, least      132
Action, variables      247
Appell      110 300
Archimedes      293
Aristotle      292
Auxiliary conditions      43 48 62 141 146
Bar, clamped      70
Bar, jointed      80
bernoulli      35 99 136 270 293
Body, rigid      103
Bohr      240 301
Boltzmann      32
Born      301
Boundary condition      68f
Boundary condition, term      120
Brachistochrone      35
Broglie, de      229 240 254 277 280
Burgers      243
Canonical equations      161
Canonical equations, integral      168 192
Canonical equations, transformations      193f
Cartan      174
Catenary      81
Cauchy      167
Cayley      170
Centre of mass      103
Circulation      209
Configuration space      12 138
Conservation of energy      31 94 120f
Conservative forces      30
Courant      68
Curvilinear coordinates      19 93
Degeneracy      152
Degree of freedom      10 126
delaunay      243f 279
Descartes      7 17
Dido      35 66
Differential, bilinear      212
Dirac      301
Displacement, reversible      74
Duhring      291
Dynamics      92
D’Alembert      76 88ff
D’Alembert, Principle of      88f 92
Effective force      90
Einstein      17 20 21 91 96 99 103 132 185 253 280
Electron microscope      268
Energy theorem      119
Eotvos      102
Epstein      301
Equilibrium      78
Equilibrium, stability of      158
Euler      3 6 36 53f 103 111 136 190 289 296
Euler, equations of      104
Euler-Lagrange, differential equation of      59 70 77 117
Euler-Lagrange, principle      190
Extremum      42
Fermat      7 35
Fermat, principle of      135 271
Force of inertia      88
Force, apparent      96
Force, generalized      27
Foucault      102 275
FOURIER      51 86
Fresnel      278 289
Galileo      139 292
Gauss      18 106f 289 299
Geiger — Scheel      292
Generalized coordinates      6 60 116
Generating function      205 228 231
Geodesic      109
Geometrical solution      264 280f
Gibbs      172
Griffith      90
Gyroscopic      122 200
Hamel      292
Hamilton      6 77 111 167 170 193 220 222f 229 255 277 291 297
Hamilton-Jacobi differential, equation of      224f 276
Heisenberg      301
Helmholtz      180 230 300
Hero      35
Hertz      25 109 130f 299 300
hilbert      51 68
Holonomic      24 85 92
Huygens, principle of      269 278 289
Ignorable variable      125
Inertia      88
Integral invariant      210
Invariance      19 115 197 201
Invariant      208 221
Isoperimetric      66
jacobi      77 111 136 193 227 229 255 291 296
Jacobi, principle of      135 138f
JORDAN      301
Kepler problem      242 248
Kinematical condition      11 23
kinetic energy      17 21 33 94
Kinosthenic variable      125
Koenig      295
Lagrange      3 6 35 53f
Lagrange, bracket      213
Lagrange, equations of      111
Lambda-method      43 49 68 83 144 188
Least action      92 132
legendre      108 161
Leibniz      36 294
Levi — Civita      240
Lie      201 216 230 300
Liouville      178
Liouville, theorem of      177
Lissajous figures      158 251
Lorentz      30
Mach      291
Mathieu      201f
Maupertuis      136 289 295
Maxwell      278
Mayer      291
Minkowski      20 21 185
moment      72
Momentum      91 121
Monogenic      30 85
Multiplier      44 48 62 141
Newton      3 21 35 77 89 91 92 107 293
Non-holonomic      24 48 65 85 146
Nordheim      291
Ostrogradski      170
Phase space      172 186
Phase space, fluid      172
Poincare      180 230 300
poisson      22 299
Poisson, bracket      215
Polygenic      30 85 92
Polygenic, forces      146
potential energy      33 94
Principal axes      151
Principal axes, function      224
Principle of d'Alembert      88f 92
Principle of least action      11
Principle of least action, constraint      106
Rankine      294
Ray      268
Reaction      85
Resultant      79
Rheonomic      32 95 124 200 206
Riemann      20
Riemannian geometry      17 138f
Rotation      78
Routh      300
Saddle point.      37
Schroedinger      229 230 279 280 301
Scleronomic      31 95 121 200 206
Separable      240f
Sommerfeld      253 280 300
STARK-effect      243 301
Statics      92
Stationary value      38
Stevinus      292
Stokes theorem      209
Synge      90
System, reference      96
System, rotating      100
Tensor      19
Thomson      131 300
Top      92
Transformation, canonical      192
Transformation, coordinate      194
Transformation, point      195
Translation      78
Variables, kinematic      92
Variables, passive      165
Variation, first      39
Variation, second      40
Variations, calculus of      35f
Varignon      293
Vibrations      147
Victorial mechanics      5f
Vinci, da      139
Virtual displacement      38
Virtual displacement, work      74 87 89
Whittaker      196 201
Wilson      253 280 301
work function      27
Zeeman-effect      243 252
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