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Birkhoff G.D. Ч Dynamical Systems
Birkhoff G.D. Ч Dynamical Systems



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Ќазвание: Dynamical Systems

јвтор: Birkhoff G.D.

язык: en

–убрика: ‘изика/ƒинамические системы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1966

 оличество страниц: 305

ƒобавлена в каталог: 07.12.2004

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Analyticity of solutions      12Ч14
Ascoli      4
Asymptotic motion to periodic motions      211Ч212 227Ч237
Asymptotic motion to recurrent motions      205Ч206
Billiard ball problem      169-79
Billiard ball problem for ellipse      248Ч255
BLISS      1
Bohr      220
Bolza      35 37
Brouwer      148 234
Cantor, G.      194
Central motions      190Ч197 202Ч204
Central motions, special      202Ч204
Central motions, transitivity and intransitivity of      205Ч208
Characteristic surface      129
Chazy      260
Clausius      iii
Closed geodesics      130 135Ч139
Closed geodesics on a special closed surface      244Ч245
Closed geodesics on convex surfaces      135Ч139
Closed geodesics on open surfaces      132Ч134
Closed geodesics on symmetric surfaces      130Ч132
Conservation of energy      14Ч19
Conservative systems      14Ч19
Conservative systems, change of variables      19Ч21
Conservative systems, subject to constraints      22
Contact transformations      53Ч55
Continuity theorems      6Ч10 10Ч12
coordinates      14Ч15
Cosserat, E. and F.      14
Degrees of freedom      14
Dissipative systems      31Ч32
Energy      23Ч25
Equations of variation      10 57Ч58
Equilibrium problem      59 60 67Ч71
Equilibrium problem, Hamiltonian case of      74Ч85
Equilibrium problem, Pfaffian case of      89Ч94
EQUIVALENCE      56
Euler      35
Existence theorem      1Ч5 10Ч12
External forces      14Ч15
Formal group      60Ч63
Formal solutions      63Ч67
Formal solutions, containing a parameter      143
Galileo      iii
Generalized equilibrium      60
Generalized equilibrium, Hamiltonian case of      85Ч89
Generalized equilibrium, normal form for      71Ч74
Generalized equilibrium, Pfaffian case of      94Ч96
Generalized equilibrium, reduction to      97Ч100
Geodesics      38Ч39 180Ч188
Geodesics in a transitive case      238Ч248
Geodesics in an integrable case      248Ч255 (see also УClosed geodesiesФ)
Goursat      1
hadamard      iv 128 130 170 211 238
Hamilton      iii
Hamiltonian principal function      52
Hamiltonian systems      50Ч53
Hamiltonian systems, Lagrangian and      50Ч53
Hamiltonian systems, normal forms of      74Ч85 85Ч89
Hamiltonian systems, transformations of      53Ч55
HamiltonТs principle      34Ч36
hilbert      130
Hill      iii 139 260
Ignorable coordinates      40Ч44
Index of invariant point      176
Instability      105 220Ч231
Instability, zones of      221Ч226
Integrability      255Ч259
Integral of energy      18 52
Integral of energy in the problem of three bodies      261Ч263
Integral of energy, conditional linear      45Ч47
Integral of energy, linear in velocities      44Ч45
Integral of energy, quadratic      48Ч50
jacobi      iii 170 248
Koopman      145
Lagrange      iii 263 264 278 285
Lagrangian systems      18Ч19
Lagrangian systems, external characterization of      25Ч31
Lagrangian systems, Hamiltonian and      50Ч53
Lagrangian systems, integrals of      41Ч50
Lagrangian systems, internal characterization of      23Ч25
Lagrangian systems, normal form of      39Ч40;
Lagrangian systems, reduction of order of      40Ч41
Lagrangian systems, regular      25
Lagrangian systems, transformation of      36Ч39
Laplace      iii
Lebesgue      248
Levi Ч Civita      iv 270 273 275
Liapounoff      122
Liouville      48
Lipschitz      5
Manifold of states of motion      143
Manifold of states of motion in problem of three bodies      270Ч275 283Ч288
Mass      23
Morse      139 170 238 246 247
Multipliers      74
Multipliers, Hamiltonian      74Ч78;
Multipliers, Pfaffian      89Ч91
Newton      iii
Non-energic systems      18
Osgood      4 138
Painleve      261
Particle      23Ч25
Particle in force field      124Ч128 146Ч149
Periodic motions      59
Periodic motions, analytic continuation of      139Ч143
Periodic motions, minimal type of      133Ч139
Periodic motions, minimum type of      128Ч132
Periodic motions, near a periodic motion      159Ч165
Periodic motions, near generalized equilibrium      150Ч154
Periodic motions, obtained by the transformation method      143Ч149
Periodic motions, role of      123Ч124;
Periodic motions, simple and multiple      142
Periodic motions, stable and unstable      209Ч215
Pfaffian systems      55
Pfaffian systems, generalized equilibrium of      97Ч100
Pfaffian systems, instability of      105
Pfaffian systems, multipliers of      89Ч91
Pfaffian systems, normal form of      91Ч96
Pfaffian systems, stability of      100Ч104
Pfaffian systems, variational principle for      55
Picard      1 13 105 122
Poinca.e      iii 74 97 105 123 139 143 190 194 223 237 255 257 260 288
PoincareТs geometric theorem      165Ч169
PoincareТs geometric theorem, application of      150Ч88
Principal function of conservative systems      17
Principle of least action      36Ч39
Principle of reciprocity      26
Problem of three bodies      260Ч261
Problem of three bodies, collision in      267Ч270
Problem of three bodies, equations of      261Ч262
Problem of three bodies, generalization of      291Ч292 (see also УRestricted Problem of Three BodiesФ)
Problem of three bodies, integrals of      262Ч263
Problem of three bodies, LagrangeТs equality in      264Ч265;
Problem of three bodies, manifold of states of motion in      270Ч275 283Ч288;
Problem of three bodies, properties of motions of      275Ч283 288Ч291
Problem of three bodies, reduction of      263Ч264 283-284;
Problem of three bodies, SundmanТs inequality in      265Ч267;
Quasi-periodic motions      218Ч220
Rayleigh      iii 26
Recurrent motions      198Ч201 204Ч205 223Ч224
Restricted problem of three bodies      145 171 260
Reversibility      27 115
Reversibility and stability      115Ч121
Rotation number      184
Signorini      130
Solution      2
Stability      97Ч122
Stability of Hamiltoman and Pfaffian systems      97
Stability of Hamiltoman in case of two degrees of freedom      220Ч227
Stability of Hamiltoman in the sense of Poisson      174 190 197
Stability of Hamiltoman, complete      105Ч115
Stability of Hamiltoman, criterion of      226Ч227
Stability of Hamiltoman, permanent      121
Stability of Hamiltoman, problem of      121 227
Stability of Hamiltoman, reversibility and      115-120
Stability of Hamiltoman, unilateral      122;
State of motion      1
Surface of section      143Ч145
Surface of section, local      151Ч152
Suudman      iv 260 261 265 270 278 283
Systems with one degree of freedom      19
Systems with two degrees of freedom      19
Systems with two degrees of freedom, integrals of      45Ч50
Systems with two degrees of freedom, motions of      150Ч185 209Ч255
Systems with two degrees of freedom, normal form for      39Ч40
Transitivity      205Ч208
Uniqueness theorems      5Ч6 10Ч12
Variational principles of dynamics      34Ч39 55Ч58
Variational principles, algebraic      33Ч34
Voss      14
Wandering motions      190Ч195
Weierstrass      261
Whittaker      iv 25 55 89 130 132 162 170 248 284
Work      14
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