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Gantmacher F. — Lectures in Analytical Mechanics
Gantmacher F. — Lectures in Analytical Mechanics

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Название: Lectures in Analytical Mechanics

Автор: Gantmacher F.

Язык: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 264

Добавлена в каталог: 31.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accelerations, generalized      41
Action, elementary      88
Action, Hamilton      88 115
Action, Lagrange      114 115
Affix (of a complex number)      200
Analytical mechanics      7 8
Angle of nutation      35
Angle of precession      35
Angle of pure rotation      35
Appell's equations      22 61
Appell's equations for nonholonomic systems      57 ff.
Aristotle      25
Associated expression (of a function)      72 73
Asymptotic stability of equilibrium position      176 ff.
Asymptotic stability of linear system, criteria of      197
Asymptotic stability, theorem on      178
Autonomous system (of differential equations)      81
Bernoulli, J.      25
Bolzano — Weierstrass lemma      179
Canonical equations      73
Canonical equations of Hamilton      71 ff.
Canonical transformation(s)      128 ff.
Canonical transformation(s), free      132 ff. 135
Canonical transformation(s), nonfree      132 133
Canonical transformation(s), nonpoint      135
Canonical transformation(s), structure of an arbitrary      152 ff.
Canonical transformation(s), univalent      131
Canonical transformation(s), valence of      131
Canonicity of transformation      163 164
Caratheodory, G.      154
Cartan, E.      8 119
Characteristic equation      190
Characteristic numbers      190
Characteristic, amplitude-phase      236 237
Characteristic, frequency      236 239
Chetayev's instability test      186
Chetayev's theorem      176
Circulation of velocity      107
Compatibility with constraints      25
Complete integral      136
Complex spectrum      238
Conditional stability      182 ff.
Conjugate kinetic focus      95
Conservation of energy, law of      77
Constrained systems      9
Constraint(s)      9
Constraint(s), "frozen"      14
Constraint(s), bilateral      12
Constraint(s), classification of      9 ff.
Constraint(s), differential      9
Constraint(s), differential stationary      11
Constraint(s), finite      9
Constraint(s), finite, integrable      10
Constraint(s), finite, stationary      11
Constraint(s), geometric      9
Constraint(s), ideal      17 ff.
Constraint(s), kinematical      9
Constraint(s), nonholonomic      11
Constraint(s), nonstationary      18
Constraint(s), semiholonomic      11
Constraint(s), taut      12
Constraint(s), unilateral      12
Contact transformations      131
Coordinates, cyclic      80 ff.
Coordinates, ignorable      80 ff.
Coordinates, kinosthenic      82
Coordinates, noncyclic      80 243
Coordinates, normal      174 210
Coordinates, position      243
Coordinates, principal      174 212
Coriolis force      52
Coupled pendulums      210
Courant, R.      219
Curl (of velocity)      107
Cyclic coordinates      80 ff.
D'Alembert's principle      30 31
Degree of stability      192
Degrees of freedom      15
Deviations      166
Dirichlet's theorem      169
Dirichlet, P.G. Lejeune      169
Displaced lines      110
Displacements, possible      13 14
Displacements, possible infinitesimal      13
Displacements, virtual      13 14
Dissipation of energy, total      53 54
Dissipative forces      51 ff.
Dissipative system      52
Dissipative system, definite      54
Donkin's theorem      74 75
Dynamical equations of Euler      64 186
Effective forces      16
Eigenvector      191
Elementary action      88
Energy integral      51
Equation, characteristic      190
Equation, frequency      205
Equation, secular      190 205 230
Equilibrium position      25 166
Equilibrium position, asymptotically stable      176
Equilibrium position, stable      166 167
Equilibrium position, unstable      167
Euler's differential equations      91
Euler's dynamical equations      64 186
Euler's equations      64 65
Euler's formula      49
Euler's theorem on homogeneous functions      76
Eulerian angles      35
Fermat's principle      115 116
Fermat, P.      115
Filter      238
Fischer, E.      219
Fluid line      107
Fluid surface      107
Free body      19
Free systems      9
Frequency equation      205
Galileo, G.      25 28
General equation of dynamics      20 ff. 30
Generalized accelerations      41
Generalized conservative system(s)      76 111
Generalized coordinates, independent      34
Generalized forces      60
Generalized integral of energy      76
Generalized momenta      71
Generalized potential      67 68
Generalized total energy      76
Generalized velocities      41 68
Generating function      131
Geodesic lines      117 118
Ghetayev, N.G.      173 176
Golden rule of mechanics      25 26
Group      128
Gyroscopic forces      51
Gyroscopic moment      53
Gyroscopically uncoupled system      246 ff.
Hamilton action      115
Hamilton — Jacobi equation      135 ff. 143
Hamilton — Ostrogradsky principle      89
Hamilton's canonical equations      102 104 106
Hamilton's equations      73
Hamilton's principal function      137—139
Hamilton's principle      88 ff.
Hamilton's principle, second form of      96 ff.
Hamilton, W.R.      73 89
Hamiltonian function      73 77 80
Hamiltonian variables      71 72 75 77
Helmholtz theorem      110
Helmholtz, H.L.F.      105
Hertz, H.      248
hessian      70 71 74 75
Hessian, small      78
Hidden motions      248
Holonomic rheonomic system      12
Holonomic scleronomic system      11
Holonomic system      11 33
Hurwitz determinant      198 199
Hurwitz polynomial      201
Hurwitz, A.      198
Huyghens, C.      28
Hwa-Chung, Lee      122
Hydrodynamical interpretation of integral invariant of mechanics      105 ff.
Hypothesis of realization of admissible reaction forces      21
Ignorable coordinates      80 ff.
Influence coefficient      224
Integral invariant(s)      8 101
Integral invariant(s) in extended coordinate space      107
Integral invariant(s) of mechanics, basic      98 ff.
Integral invariant(s), absolute      122
Integral invariant(s), relative      121
Integral invariant(s), universal      122
Integral invariant(s), universal relative      122
Integral of equations of motion      83
Invariance of Poincare integral, geometrical interpretation of      120
Invariance of volume in phase space      125 ff.
Jacobi equations      114
Jacobi theorem      136
Jacobi — Poisson theorem      85
Jacobi, K.G.J.      84 114
Jacobian      71 74
Jacobian functional matrix      47
Jacobian matrix of order n      161
Jacobian matrix, simplicial nature of      161
Kepler's three laws of planetary motion      148
Keplerian motion      146 147
Kinetic potential      66
Kinosthenic coordinates      82
Kronecker's symbol      160 189
Lagrange action      114 115
Lagrange brackets      160
Lagrange's equations for potential forces      66 ff.
Lagrange's equations in independent coordinates      41
Lagrange's equations of the first kind      22
Lagrange's equations of the second kind      22 63
Lagrange's equations of the second kind in independent coordinates      40 ff.
Lagrange's equations, investigations of      45 ff.
Lagrange's theorem      169 171
Lagrange's theorem on stability of equilibrium position      166 ff.
Lagrange, J.L.      22 115 169 210
Lagrangian function      66 73 245
Lagrangian variables      71 72 75 78
Landau, L.      86
Legendre transformation      74
Lienard — Chipart conditions      199
Lienard — Chipart criterion      201
Linear approximation for nonlinear system      193
Liouville's theorem      127 150
Lorentz fores      68
Lyapunov function      182 254
Lyapunov's first theorem      174
Lyapunov's second theorem      176
Lyapunov's theorem      184 185
Lyapunov's theorem, corollary to      184 185
Lyapunov, A.M.      173 176 181 193
Malkin, I.G.      176
Matrix, generalized-simplicial      163
Matrix, oscillatory      225
Matrix, positive definite      205
Matrix, simplicial      162
Maupertuis, P.      115
Maupertuis-Lagrange principle of least action      114 ff.
Maximinimal properties      219
Maxwell's principle of reciprocity      224
Mersenne law      227
Mikhailov's criterion      200
Mikhailov, A.V.      200
Minimaximal properties      219
Natural systems      70
Newton's law of gravitation      148
Nodal line      35
Noncyclic coordinates      80 243
Nonholonomic system      11 12
Nonnatural system      70
Normal coordinates      174 210
Optical principle of Fermat      115 116
Oscillations, forced      216 236
Oscillations, free      216
Oscillatory matrix      225
Ostrogradsky, M.V.      89
Paths, circuitous      89
Paths, straight-line      89
Perturbation theory, application of canonical transformations to      150 ff.
Poincare integral      121
Poincare — Cartan integral      101 104 106 121 129
Poincare — Cartan integral invariant      98 ff.
Poincare, J.H.      8 119 193
Point transformation      135
Poisson bracket(s)      83 ff. 160
Poisson bracket(s), invariance of, in canonical transformation      163 ff.
Poisson identity      84
Poisson, S.D.      84
Position coordinates      243
potential energy      48
Potential forces      48
Potential of forces      48
Power of nonpotential forces      50
Principal coordinates      174 212
Principal oscillations      210
Principle of least action of Maupertuis — Lagrange      114 115
Principle of possible displacements      25 29
Principle of reciprocity, Maxwell's      224
Principle of virtual displacements      25 26 30 39
Pseudoaccelerations      60 62
Pseudocoordinates      59
Pseudovelocities      59
Pyatigorsky, L.      86
Rayleigh's dissipative function      53 231
Rayleigh's functions      233
Rayleigh's theorem      220
Rayleigh, J.W.      220
Reaction forces of constraints      16
Reduced system      246
Resonance      216
Rheonomic system      11
Rose, H.V.      115
Rotor (of velocity)      107
Routh equations      78 ff. 80 81
Routh functions      80 81 244
Routh potential      245 246 252 257
Routh variables      78 242 243
Routh — Hurwitz condition      199
Routh, E.      198 243 245 254 256
Scleronomic system      11 35
Secular equation      190 205 230
Secular terms      192 209
Separation of variables, method of      141 ff.
Separation theorem      221
Shortest lines in space      118
Simplicial group      162
Simplicial matrix      162
Solution, asymptotically stable      185
Solution, stable      185
Spectrum, complex      238
Stability of linear systems      189 ff.
Stability of stationary motions      252 ff.
Stability, geometric criterion of      200
Stationary motion, conditions for existence of      255
Stationary motion, criterion of stability of      254 256
Stationary motion, stability of      252 ff.
Stationary motion, stable      254 255
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