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Mathematics Subject Classification – MSC2020

Mechanics of particles and systems {For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX} 65313

70-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of particles and systems 173

70-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems 1238

70-02

Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems 1064

70-03

History of mechanics of particles and systems [Consider also classification numbers pertaining to Section 01-XX] 1277

70-04

Software, source code, etc. for problems pertaining to mechanics of particles and systems 346

70-05

Experimental work for problems pertaining to mechanics of particles and systems 318

70-06

Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems 736

70-08

Computational methods for problems pertaining to mechanics of particles and systems 3059

70-10

Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems 20

70-11

Research data for problems pertaining to mechanics of particles and systems 0

70Axx

Axiomatics, foundations 784

70A05

Axiomatics, foundations 775

70A99

None of the above, but in this section 6

70Bxx

Kinematics [See also 53A17] 6338

70B05

Kinematics of a particle 288

70B10

Kinematics of a rigid body 696

70B15

Kinematics of mechanisms and robots [See also 68T40, 70Q05, 93C85] 5206

70B99

None of the above, but in this section 226

70Cxx

Statics 606

70C20

Statics 595

70C99

None of the above, but in this section 4

70Exx

Dynamics of a rigid body and of multibody systems 10536

70E05

Motion of the gyroscope 1609

70E15

Free motion of a rigid body [See also 70M20] 2411

70E17

Motion of a rigid body with a fixed point 651

70E18

Motion of a rigid body in contact with a solid surface [See also 70F25] 522

70E20

Perturbation methods for rigid body dynamics 214

70E40

Integrable cases of motion in rigid body dynamics 424

70E45

Higher-dimensional generalizations in rigid body dynamics 55

70E50

Stability problems in rigid body dynamics 659

70E55

Dynamics of multibody systems 1898

70E60

Robot dynamics and control of rigid bodies [See also 68T40, 70Q05, 93C85] 2128

70E99

None of the above, but in this section 1058

70Fxx

Dynamics of a system of particles, including celestial mechanics 15055

70F05

Two-body problems 1323

70F07

Three-body problems 2467

70F10

\(n\)-body problems 2595

70F15

Celestial mechanics 5122

70F16

Collisions in celestial mechanics, regularization 181

70F17

Inverse problems for systems of particles 121

70F20

Holonomic systems related to the dynamics of a system of particles 803

70F25

Nonholonomic systems related to the dynamics of a system of particles 1905

70F35

Collision of rigid or pseudo-rigid bodies 688

70F40

Problems involving a system of particles with friction 653

70F45

The dynamics of infinite particle systems 165

70F99

None of the above, but in this section 1406

70Gxx

General models, approaches, and methods [See also 37-XX] 4396

70G10

Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics 1256

70G40

Topological and differential topological methods for problems in mechanics 102

70G45

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics [See also 53Cxx, 53Dxx, 58Axx] 1613

70G55

Algebraic geometry methods for problems in mechanics 69

70G60

Dynamical systems methods for problems in mechanics 146

70G65

Symmetries, Lie group and Lie algebra methods for problems in mechanics 586

70G70

Functional analytic methods for problems in mechanics 12

70G75

Variational methods for problems in mechanics 280

70G99

None of the above, but in this section 534

70Hxx

Hamiltonian and Lagrangian mechanics [See also 37Jxx] 14748

70H03

Lagrange’s equations 2198

70H05

Hamilton’s equations 4113

70H06

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics 1165

70H07

Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics 187

70H08

Nearly integrable Hamiltonian systems, KAM theory 546

70H09

Perturbation theories for problems in Hamiltonian and Lagrangian mechanics 261

70H11

Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics 172

70H12

Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics 322

70H14

Stability problems for problems in Hamiltonian and Lagrangian mechanics 349

70H15

Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 763

70H20

Hamilton-Jacobi equations in mechanics 1181

70H25

Hamilton’s principle 599

70H30

Other variational principles in mechanics 544

70H33

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics 1525

70H40

Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics 1249

70H45

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx] 636

70H50

Higher-order theories for problems in Hamiltonian and Lagrangian mechanics 122

70H99

None of the above, but in this section 1066

70Jxx

Linear vibration theory 3167

70J10

Modal analysis in linear vibration theory 581

70J25

Stability for problems in linear vibration theory 607

70J30

Free motions in linear vibration theory 493

70J35

Forced motions in linear vibration theory 311

70J40

Parametric resonances in linear vibration theory 120

70J50

Systems arising from the discretization of structural vibration problems 198

70J99

None of the above, but in this section 1038

70Kxx

Nonlinear dynamics in mechanics [See also 34Cxx, 37-XX] 11009

70K05

Phase plane analysis, limit cycles for nonlinear problems in mechanics 704

70K20

Stability for nonlinear problems in mechanics 2796

70K25

Free motions for nonlinear problems in mechanics 155

70K28

Parametric resonances for nonlinear problems in mechanics 343

70K30

Nonlinear resonances for nonlinear problems in mechanics 1027

70K40

Forced motions for nonlinear problems in mechanics 1624

70K42

Equilibria and periodic trajectories for nonlinear problems in mechanics 407

70K43

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics 243

70K44

Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics 217

70K45

Normal forms for nonlinear problems in mechanics 146

70K50

Bifurcations and instability for nonlinear problems in mechanics 1779

70K55

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics [See also 37D45] 1083

70K60

General perturbation schemes for nonlinear problems in mechanics 228

70K65

Averaging of perturbations for nonlinear problems in mechanics 217

70K70

Systems with slow and fast motions for nonlinear problems in mechanics 221

70K75

Nonlinear modes 118

70K99

None of the above, but in this section 1772

70Lxx

Random and stochastic aspects of the mechanics of particles and systems 1495

70L05

Random vibrations in mechanics of particles and systems [See also 74H50] 1493

70L10

Stochastic geometric mechanics 2

70L99

None of the above, but in this section 0

70Mxx

Orbital mechanics 3325

70M20

Orbital mechanics 3316

70M99

None of the above, but in this section 4

70Pxx

Variable mass, rockets 799

70P05

Variable mass, rockets 798

70P99

None of the above, but in this section 1

70Qxx

Control of mechanical systems [See also 60Gxx, 60Jxx] 5695

70Q05

Control of mechanical systems 5692

70Q99

None of the above, but in this section 0

70Sxx

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 2795

70S05

Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 1047

70S10

Symmetries and conservation laws in mechanics of particles and systems 345

70S15

Yang-Mills and other gauge theories in mechanics of particles and systems 1143

70S20

More general nonquantum field theories in mechanics of particles and systems 107

70S99

None of the above, but in this section 59

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Mathematics Subject Classification – MSC2020

Overview