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Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx] 1489

70G55

Algebraic geometry methods 64

70G60

Dynamical systems methods 120

70G65

Symmetries, Lie-group and Lie-algebra methods 502

70G70

Functional-analytic methods 12

70G75

Variational methods 235

70G99

None of the above, but in this section 531

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 13856

70H03

Lagrange’s equations 2089

70H05

Hamilton’s equations 3987

70H06

Completely integrable systems and methods of integration 1061

70H07

Nonintegrable systems 176

70H08

Nearly integrable Hamiltonian systems, KAM theory 470

70H09

Perturbation theories 228

70H11

Adiabatic invariants 149

70H12

Periodic and almost periodic solutions 255

70H14

Stability problems 297

70H15

Canonical and symplectic transformations 738

70H20

Hamilton-Jacobi equations 1104

70H25

Hamilton’s principle 581

70H30

Other variational principles 512

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 1353

70H40

Relativistic dynamics 1166

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 580

70H50

Higher-order theories 111

70H99

None of the above, but in this section 1068

70Jxx

Linear vibration theory 3064

Modal analysis 551

Stability 588

Free motions 488

Forced motions 299

Parametric resonances 108

70J50

Systems arising from the discretization of structural vibration problems 177

70J99

None of the above, but in this section 1027

70Kxx

Nonlinear dynamics [See also 34Cxx, 37-XX] 10285

70K05

Phase plane analysis, limit cycles 675

70K20

Stability 2711

70K25

Free motions 148

70K28

Parametric resonances 299

70K30

Nonlinear resonances 946

70K40

Forced motions 1528

70K42

Equilibria and periodic trajectories 356

70K43

Quasi-periodic motions and invariant tori 187

70K44

Homoclinic and heteroclinic trajectories 190

70K45

Normal forms 125

70K50

Bifurcations and instability 1640

70K55

Transition to stochasticity (chaotic behavior) [See also 37D45] 974

70K60

General perturbation schemes 208

70K65

Averaging of perturbations 185

70K70

Systems with slow and fast motions 173

70K75

Nonlinear modes 89

70K99

None of the above, but in this section 1745

70Lxx

Random vibrations [See also 74H50] 1451

70L05

Random vibrations [See also 74H50] 1450

70L99

None of the above, but in this section 1

70Mxx

Orbital mechanics 3141

70M20

Orbital mechanics 3136

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 732

70P05

Variable mass, rockets 731

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5249

70Q05

Control of mechanical systems [See also 60Gxx, 60Jxx] 5247

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2246

70S05

Lagrangian formalism and Hamiltonian formalism 919

70S10

Symmetries and conservation laws 280

70S15

Yang-Mills and other gauge theories 763

70S20

More general nonquantum field theories 89

70S99

None of the above, but in this section 55

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