|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gantmacher F. — Lectures in Analytical Mechanics |
|
|
|
| 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте