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Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx] 1513

70G55

Algebraic geometry methods 65

70G60

Dynamical systems methods 130

70G65

Symmetries, Lie-group and Lie-algebra methods 519

70G70

Functional-analytic methods 12

70G75

Variational methods 240

70G99

None of the above, but in this section 532

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 14064

70H03

Lagrange’s equations 2126

70H05

Hamilton’s equations 4023

70H06

Completely integrable systems and methods of integration 1083

70H07

Nonintegrable systems 177

70H08

Nearly integrable Hamiltonian systems, KAM theory 481

70H09

Perturbation theories 240

70H11

Adiabatic invariants 155

70H12

Periodic and almost periodic solutions 267

70H14

Stability problems 306

70H15

Canonical and symplectic transformations 743

70H20

Hamilton-Jacobi equations 1116

70H25

Hamilton’s principle 582

70H30

Other variational principles 519

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 1410

70H40

Relativistic dynamics 1192

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 600

70H50

Higher-order theories 116

70H99

None of the above, but in this section 1066

70Jxx

Linear vibration theory 3088

Modal analysis 558

Stability 594

Free motions 489

Forced motions 304

Parametric resonances 111

70J50

Systems arising from the discretization of structural vibration problems 180

70J99

None of the above, but in this section 1030

70Kxx

Nonlinear dynamics [See also 34Cxx, 37-XX] 10372

70K05

Phase plane analysis, limit cycles 675

70K20

Stability 2724

70K25

Free motions 149

70K28

Parametric resonances 301

70K30

Nonlinear resonances 954

70K40

Forced motions 1540

70K42

Equilibria and periodic trajectories 368

70K43

Quasi-periodic motions and invariant tori 197

70K44

Homoclinic and heteroclinic trajectories 194

70K45

Normal forms 132

70K50

Bifurcations and instability 1657

70K55

Transition to stochasticity (chaotic behavior) [See also 37D45] 993

70K60

General perturbation schemes 215

70K65

Averaging of perturbations 188

70K70

Systems with slow and fast motions 175

70K75

Nonlinear modes 90

70K99

None of the above, but in this section 1750

70Lxx

Random vibrations [See also 74H50] 1460

70L05

Random vibrations [See also 74H50] 1459

70L99

None of the above, but in this section 1

70Mxx

Orbital mechanics 3180

70M20

Orbital mechanics 3173

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 767

70P05

Variable mass, rockets 766

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5336

70Q05

Control of mechanical systems [See also 60Gxx, 60Jxx] 5334

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2318

70S05

Lagrangian formalism and Hamiltonian formalism 954

70S10

Symmetries and conservation laws 289

70S15

Yang-Mills and other gauge theories 797

70S20

More general nonquantum field theories 93

70S99

None of the above, but in this section 57

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