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Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx] 1502

70G55

Algebraic geometry methods 64

70G60

Dynamical systems methods 125

70G65

Symmetries, Lie-group and Lie-algebra methods 512

70G70

Functional-analytic methods 12

70G75

Variational methods 240

70G99

None of the above, but in this section 533

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 13999

70H03

Lagrange’s equations 2117

70H05

Hamilton’s equations 4008

70H06

Completely integrable systems and methods of integration 1076

70H07

Nonintegrable systems 177

70H08

Nearly integrable Hamiltonian systems, KAM theory 472

70H09

Perturbation theories 236

70H11

Adiabatic invariants 155

70H12

Periodic and almost periodic solutions 263

70H14

Stability problems 302

70H15

Canonical and symplectic transformations 740

70H20

Hamilton-Jacobi equations 1108

70H25

Hamilton’s principle 583

70H30

Other variational principles 517

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 1401

70H40

Relativistic dynamics 1186

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 593

70H50

Higher-order theories 115

70H99

None of the above, but in this section 1066

70Jxx

Linear vibration theory 3075

Modal analysis 555

Stability 589

Free motions 489

Forced motions 300

Parametric resonances 110

70J50

Systems arising from the discretization of structural vibration problems 177

70J99

None of the above, but in this section 1029

70Kxx

Nonlinear dynamics [See also 34Cxx, 37-XX] 10333

70K05

Phase plane analysis, limit cycles 674

70K20

Stability 2718

70K25

Free motions 148

70K28

Parametric resonances 301

70K30

Nonlinear resonances 951

70K40

Forced motions 1540

70K42

Equilibria and periodic trajectories 365

70K43

Quasi-periodic motions and invariant tori 194

70K44

Homoclinic and heteroclinic trajectories 193

70K45

Normal forms 128

70K50

Bifurcations and instability 1648

70K55

Transition to stochasticity (chaotic behavior) [See also 37D45] 983

70K60

General perturbation schemes 212

70K65

Averaging of perturbations 187

70K70

Systems with slow and fast motions 176

70K75

Nonlinear modes 89

70K99

None of the above, but in this section 1748

70Lxx

Random vibrations [See also 74H50] 1455

70L05

Random vibrations [See also 74H50] 1454

70L99

None of the above, but in this section 1

70Mxx

Orbital mechanics 3161

70M20

Orbital mechanics 3154

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 755

70P05

Variable mass, rockets 754

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5291

70Q05

Control of mechanical systems [See also 60Gxx, 60Jxx] 5289

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2291

70S05

Lagrangian formalism and Hamiltonian formalism 942

70S10

Symmetries and conservation laws 286

70S15

Yang-Mills and other gauge theories 784

70S20

More general nonquantum field theories 89

70S99

None of the above, but in this section 56

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