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Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx] 1569

70G55

Algebraic geometry methods 68

70G60

Dynamical systems methods 137

70G65

Symmetries, Lie-group and Lie-algebra methods 566

70G70

Functional-analytic methods 12

70G75

Variational methods 262

70G99

None of the above, but in this section 536

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 14439

70H03

Lagrange’s equations 2166

70H05

Hamilton’s equations 4079

70H06

Completely integrable systems and methods of integration 1128

70H07

Nonintegrable systems 184

70H08

Nearly integrable Hamiltonian systems, KAM theory 525

70H09

Perturbation theories 250

70H11

Adiabatic invariants 161

70H12

Periodic and almost periodic solutions 283

70H14

Stability problems 326

70H15

Canonical and symplectic transformations 752

70H20

Hamilton-Jacobi equations 1153

70H25

Hamilton’s principle 593

70H30

Other variational principles 537

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 1462

70H40

Relativistic dynamics 1225

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 625

70H50

Higher-order theories 121

70H99

None of the above, but in this section 1064

70Jxx

Linear vibration theory 3125

Modal analysis 568

Stability 599

Free motions 492

Forced motions 306

Parametric resonances 114

70J50

Systems arising from the discretization of structural vibration problems 190

70J99

None of the above, but in this section 1034

70Kxx

Nonlinear dynamics [See also 34Cxx, 37-XX] 10614

70K05

Phase plane analysis, limit cycles 689

70K20

Stability 2746

70K25

Free motions 152

70K28

Parametric resonances 313

70K30

Nonlinear resonances 967

70K40

Forced motions 1573

70K42

Equilibria and periodic trajectories 382

70K43

Quasi-periodic motions and invariant tori 225

70K44

Homoclinic and heteroclinic trajectories 210

70K45

Normal forms 139

70K50

Bifurcations and instability 1691

70K55

Transition to stochasticity (chaotic behavior) [See also 37D45] 1018

70K60

General perturbation schemes 219

70K65

Averaging of perturbations 204

70K70

Systems with slow and fast motions 191

70K75

Nonlinear modes 99

70K99

None of the above, but in this section 1757

70Lxx

Random vibrations [See also 74H50] 1471

70L05

Random vibrations [See also 74H50] 1470

70L99

None of the above, but in this section 0

70Mxx

Orbital mechanics 3233

70M20

Orbital mechanics 3226

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 790

70P05

Variable mass, rockets 789

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5502

70Q05

Control of mechanical systems [See also 60Gxx, 60Jxx] 5500

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2577

70S05

Lagrangian formalism and Hamiltonian formalism 1006

70S10

Symmetries and conservation laws 328

70S15

Yang-Mills and other gauge theories 973

70S20

More general nonquantum field theories 102

70S99

None of the above, but in this section 57

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