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Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx] 1523

70G55

Algebraic geometry methods 66

70G60

Dynamical systems methods 132

70G65

Symmetries, Lie-group and Lie-algebra methods 534

70G70

Functional-analytic methods 12

70G75

Variational methods 246

70G99

None of the above, but in this section 533

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 14146

70H03

Lagrange’s equations 2135

70H05

Hamilton’s equations 4030

70H06

Completely integrable systems and methods of integration 1090

70H07

Nonintegrable systems 178

70H08

Nearly integrable Hamiltonian systems, KAM theory 494

70H09

Perturbation theories 242

70H11

Adiabatic invariants 156

70H12

Periodic and almost periodic solutions 270

70H14

Stability problems 308

70H15

Canonical and symplectic transformations 744

70H20

Hamilton-Jacobi equations 1125

70H25

Hamilton’s principle 585

70H30

Other variational principles 521

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 1428

70H40

Relativistic dynamics 1196

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 611

70H50

Higher-order theories 118

70H99

None of the above, but in this section 1066

70Jxx

Linear vibration theory 3092

Modal analysis 559

Stability 595

Free motions 489

Forced motions 304

Parametric resonances 112

70J50

Systems arising from the discretization of structural vibration problems 180

70J99

None of the above, but in this section 1032

70Kxx

Nonlinear dynamics [See also 34Cxx, 37-XX] 10441

70K05

Phase plane analysis, limit cycles 678

70K20

Stability 2734

70K25

Free motions 150

70K28

Parametric resonances 304

70K30

Nonlinear resonances 959

70K40

Forced motions 1548

70K42

Equilibria and periodic trajectories 372

70K43

Quasi-periodic motions and invariant tori 205

70K44

Homoclinic and heteroclinic trajectories 197

70K45

Normal forms 133

70K50

Bifurcations and instability 1668

70K55

Transition to stochasticity (chaotic behavior) [See also 37D45] 1000

70K60

General perturbation schemes 218

70K65

Averaging of perturbations 194

70K70

Systems with slow and fast motions 178

70K75

Nonlinear modes 95

70K99

None of the above, but in this section 1751

70Lxx

Random vibrations [See also 74H50] 1464

70L05

Random vibrations [See also 74H50] 1463

70L99

None of the above, but in this section 1

70Mxx

Orbital mechanics 3199

70M20

Orbital mechanics 3192

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 774

70P05

Variable mass, rockets 773

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5387

70Q05

Control of mechanical systems [See also 60Gxx, 60Jxx] 5385

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2386

70S05

Lagrangian formalism and Hamiltonian formalism 977

70S10

Symmetries and conservation laws 300

70S15

Yang-Mills and other gauge theories 832

70S20

More general nonquantum field theories 96

70S99

None of the above, but in this section 57

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