Classical Mechanics  

In General > s.a. history of physics; state.
* Idea: The class of physical theories in which the system has a well-defined history, with dynamics described by (differential or functional) equations of motion on a configuration space C (infinite-dimensional in field theory); The logical structure is that of a Boolean lattice.
* History: Since the 1970s, when it was realized that chaos arises even with few degrees of freedom in non-linear systems, the perspective in the field has changed.
* Subjects of interest: Various general aspects of non-linear dynamical systems, like chaos and turbulence.
* Important recent applications: Galaxy formation; Saturn ring structure.

Related Topics
> Approaches: see formulations [including dynamical systems]; hamiltonian dynamics; lagrangian dynamics.
> Concepts: see Degrees of Freedom; energy; entropy; force; inertia; information; statistical mechanics; time; Trajectory.
> Systems: see classical systems; field theory.
> Phenomena: see chaos; Friction.
> Results: see Bertrand's Theorem; noether theorem; Work-Energy Theorem.

Variations and Generalizations > s.a. hilbert space; higher-order lagrangians; MOND.
* Standard ones: Special and general relativistic dynamics; Quantum dynamics.
* And quantum theory: Quantum corrections, if taken into account, introduce modifications to classical dynamics.
* Barbour-Bertotti: Classical, without the ideal elements of inertial frames and external time (> see parametrized theories).
* Super classical quantum mechanics: A proposed theory which is equivalent to the Heisenberg, Schrödinger, and Dirac non-relativistic quantum mechanics, with the addition of Born's probabilistic interpretation of the wave function built in from the start.
@ Relationship with special and general relativity: Havas RMP(64); NCB 102(88)495 [Newton's third law].
@ Relationship with quantum mechanics: Savickas AJP(02)aug [and general relativity]; Valentini PLA(04)qp/03 [non-quantum systems]; Bojowald et al PRD(12)-a1208 [higher time derivatives in effective dynamics]; Kurihara et al JTAP(14)-a1312 [classical mechanics as an equilibrium state of statistical mechanics]; Dittrich & Reuter 20.
@ Quantum corrections: Bouda & Djama PLA(01) [second law]; Ward MPLA(02); Vachaspati PRD(17)-a1704 [coherent state coupled to a quantum bath].
@ Post-Newtonian: Chicone gq/01-conf [equations of motion are functional differential equations].
@ Nambu mechanics: Lassig & Joshi LMP(97) [constrained systems]; > s.a. poisson structure.
@ Supermechanics, anticommuting degrees of freedom: Cariñena & Figueroa JPA(97) [Hamiltonian and Lagrangian]; Bruce et al JGM(17)-a1606 [geometric].
@ Other examples: Salesi IJMPA(02)qp/01 [spinning particles].
@ Stochastic: Guerra PRP(81); Streater RPMP(93) [and Markov chains]; Zambrini a1212 [path-integral inspired stochastic deformation of Lagrangian and Hamiltonian approaches]; > s.a. stochastic processes.
@ Other generalizations: Lamb AJP(01)apr [super-classical quantum mechanics]; Kisil JPA(04)qp/02, Brodlie & Kisil in(03)qp, Brodlie JMP(04) [p-mechanics]; Khrennikov & Nilsson 04 [p-adic; r BAMS(06)]; Kisil RPMP(05) [p-mechanics and field theory]; Lämmerzahl & Rademaker PRD(12)-a0904 [higher-order equations of motion]; García-Morales CNSNS(16)-a1507 [semipredictable]; Chashchina IJMPD(20)-a1902 [Planck-scale modification]; > s.a. conformal invariance.

References > s.a. BRST transformations; parametrized systems [including relationalism]; spacetime; topological field theories.
@ Resources: issue AJP(00)apr [reviews].
@ Texts: Hertz re-56 [classic]; Mercier 59; Bergmann 62 [I]; Pars 65; Aharoni 72; Desloge 82; Raychaudhuri 83; Griffiths 85; Fowles 86; Kibble 86; Reichert 90; Matzner & Shepley 91; Marsden 92; Barger & Olsson 95; Marion & Thornton 95; Hestenes 99; Teodorescu 07, 08, 09 [comprehensive]; Helliwell & Sahakian 21.
@ Texts, II: Chow 95; Kibble & Berkshire 04; Taylor 05; Morin 08; Verma 09; Johnson 10; Kleppner & Kolenkow 10 [II advanced]; Chaichian et al 12; Chow 13; Rajeev 13; Englert 15; Iro 15; Nolte 15 [geometry, non-linear dynamics, complex systems, networks, relativity; r PT(15)]; Bettini 16; Nolting 16; Ilisie 20.
@ Texts, III: Synge & Griffith 59; Saletan & Cromer 71; Sudarshan & Mukunda 75; Abraham & Marsden 78; Goldstein 80; Gallavotti 83; Woodhouse 87; Arnold 89; Calkin 96 [Lagrangian and Hamiltonian]; Thirring 97; Hand & Finch 98; Corinaldesi 99; Greiner 02; Fasano & Marmi 06; DiBenedetto 10; Shapiro & de Berredo-Peixoto 13; Lemos 18; Leinaas 19.
@ Geometrical emphasis: Marmo et al 85; Giachetta et al 10; Holm 11; Lessig a1206 [primer].
@ (Non-)integrability, chaos: Katok & Hasselblatt 95; McCauley 97; Scheck 10.
@ Problems and solutions: Tonti 77 [method]; Lim 94; de Lange & Pierrus 10.
@ Other emphasis: Lanczos 49 [variational methods]; Rasband 83, Abraham & Ratiu 94 [symmetries]; José & Saletan 98; Johns 05 [relativity and quantum mechanics]; Müller-Kirsten 08 [relativity]; Thorne & Blandford 15 [applications]; Sussman & Wisdom 15 [conceptual-computational]; Hentschke 17 [numerical, theory of elasticity, engineering applications]; > s.a. computational physics.
@ Foundations: Hesse AJP(64)dec [philosophical]; Desloge AJP(89)aug; Gallavotti in(06)mp/05; Darrigol SHPMP(07) [necessary nature]; Preston SHPSA(08) [Mach and Hertz]; Sklar 13; Hartmann a1307-PhD; Alonso-Blanco & Muñoz-Díaz a1404, a1411; Lubashevsky a1603 [from "microlevel reducibility"].
> Online resources: Internet Encyclopedia of Science pages.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 12 jan 2021